Chapter 3 Resource Masters - Morgan Park High School · 2009. 12. 2. · ©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 3 Resource Masters The Fast

Chapter 3Resource Masters

Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.

Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7

ANSWERS FOR WORKBOOKS The answers for Chapter 3 of these workbookscan be found in the back of this Chapter Resource Masters booklet.

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027

ISBN: 0-07-827727-2 Algebra 1Chapter 3 Resource Masters

2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03

Glencoe/McGraw-Hill

© Glencoe/McGraw-Hill iii Glencoe Algebra 1

Contents

Vocabulary Builder . . . . . . . . . . . . . . . . vii

Lesson 3-1Study Guide and Intervention . . . . . . . . 137–138Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 139Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Reading to Learn Mathematics . . . . . . . . . . 141Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 142









Chapter 3 AssessmentChapter 3 Test, Form 1 . . . . . . . . . . . . 191–192Chapter 3 Test, Form 2A . . . . . . . . . . . 193–194Chapter 3 Test, Form 2B . . . . . . . . . . . 195–196Chapter 3 Test, Form 2C . . . . . . . . . . . 197–198Chapter 3 Test, Form 2D . . . . . . . . . . . 199–200Chapter 3 Test, Form 3 . . . . . . . . . . . . 201–202Chapter 3 Open-Ended Assessment . . . . . . 203Chapter 3 Vocabulary Test/Review . . . . . . . 204Chapter 3 Quizzes 1 & 2 . . . . . . . . . . . . . . . 205Chapter 3 Quizzes 3 & 4 . . . . . . . . . . . . . . . 206Chapter 3 Mid-Chapter Test . . . . . . . . . . . . 207Chapter 3 Cumulative Review . . . . . . . . . . . 208Chapter 3 Standardized Test Practice . . 209–210Unit 1 Test/Review (Ch. 1–3) . . . . . . . . 211–212

Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1

ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A39

© Glencoe/McGraw-Hill iv Glencoe Algebra 1

Teacher’s Guide to Using theChapter 3 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 3 Resource Masters includes the core materials neededfor Chapter 3. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.

Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

WHEN TO USE Give these pages tostudents before beginning Lesson 3-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.

Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.

WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.

WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.

Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.

WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.

WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.

© Glencoe/McGraw-Hill v Glencoe Algebra 1

Assessment OptionsThe assessment masters in the Chapter 3Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions

and is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-response Bonus question.

• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.

• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questionsthat appear in the Student Edition onpages 186–187. This improves students’familiarity with the answer formats theymay encounter in test taking.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided forthe assessment masters in this booklet.

Reading to Learn MathematicsVocabulary Builder

NAME ______________________________________________ DATE ____________ PERIOD _____

33

© Glencoe/McGraw-Hill vii Glencoe Algebra 1

Voca

bula

ry B

uild

erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 3.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.

Vocabulary Term Found on Page Definition/Description/Example

consecutive integers

kuhn-SEH-kyuh-tihv

defining a variable

dimensional analysis

duh·MEHNCH·nuhl

equivalent equation

ih·KWIHV·luhnt

extremes

formula

identity

means

multi-step equations

(continued on the next page)

© Glencoe/McGraw-Hill viii Glencoe Algebra 1

Vocabulary Term Found on Page Definition/Description/Example

number theory

percent of change

percent of decrease

percent of increase

proportion

pruh·POHR·shun

ratio

rate

scale

solve an equation

weighted average

work backward

Reading to Learn MathematicsVocabulary Builder (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

33

Study Guide and InterventionWriting Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1

© Glencoe/McGraw-Hill 137 Glencoe Algebra 1

Less

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Write Equations Writing equations is one strategy for solving problems. You can use avariable to represent an unspecified number or measure referred to in a problem. Then youcan write a verbal expression as an algebraic expression.

Translate eachsentence into an equation or aformula.

a. Ten times a number x is equal to2.8 times the difference y minus z.10 � x � 2.8 � ( y � z)The equation is 10x � 2.8( y � z).

b. A number m minus 8 is the sameas a number n divided by 2.m � 8 � n � 2The equation is m � 8 � .

c. The area of a rectangle equals thelength times the width. Translatethis sentence into a formula.Let A � area, � � length, and w � width.Formula: Area equals length timeswidth.A � � � wThe formula for the area of arectangle is A � �w.

n�2

Use the Four-Step Problem-Solving Plan.The population of the United States in 2001was about 284,000,000, and the land area ofthe United States is about 3,500,000 squaremiles. Find the average number of peopleper square mile in the United States.Source: www.census.gov

Step 1 Explore You know that there are284,000,000 people. You want to knowthe number of people per square mile.

Step 2 Plan Write an equation to represent thesituation. Let p represent the number ofpeople per square mile.3,500,000 � p � 284,000,000

Step 3 Solve 3,500,000 � p � 284,000,000.3,500,000p � 284,000,000 Divide each side by

p � 81.14 3,500,000.

There about 81 people per square mile.Step 4 Examine If there are 81 people per

square mile and there are 3,500,000square miles, 81 � 3,500,000 �283,500,000, or about 284,000,000 people.The answer makes sense.

Example 1Example 1 Example 2Example 2

ExercisesExercises

Translate each sentence into an equation or formula.

1. Three times a number t minus twelve equals forty.

2. One-half of the difference of a and b is 54.

3. Three times the sum of d and 4 is 32.

4. The area A of a circle is the product of � and the radius r squared.

WEIGHT LOSS For Exercises 5–6, use the following information.

Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. Hewants to weigh 150 pounds.

5. If p represents the number of pounds he wants to lose, write an equation to representthis situation.

6. How many pounds does he need to lose to reach his goal?


Write Verbal Sentences You can translate equations into verbal sentences.

Translate each equation into a verbal sentence.

a. 4n � 8 � 12.

4n � 8 � 12Four times n minus eight equals twelve.

b. a2 � b2 � c2

a2 � b2 � c2

The sum of the squares of a and b is equal to the square of c.


1. 4a � 5 � 23 2. 10 � k � 4k

3. 6xy � 24 4. x2 � y2 � 8

5. p � 3 � 2p 6. b � (h � 1)

7. 100 � 2x � 80 8. 3(g � h) � 12

9. p2 � 2p � 9 10. C � (F � 32)

11. V � Bh 12. A � hb1�2

1�3

5�9

1�3

Study Guide and Intervention (continued)

Writing Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1

ExampleExample

ExercisesExercises

Skills PracticeWriting Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1


Less

on

3-1

Translate each sentence into an equation.

1. Two added to three times a number m is the same as 18.

2. Twice a increased by the cube of a equals b.

3. Seven less than the sum of p and q is as much as 6.

4. The sum of x and its square is equal to y times z.

5. Four times the sum of f and g is identical to six times g.

Translate each sentence into a formula.

6. The perimeter P of a square equals four times the length of a side s.

7. The area A of a square is the length of a side s squared.

8. The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.

9. The area A of a circle is pi times the radius r squared.

10. The volume V of a rectangular prism equals the product of the length �, the width w,and the height h.


11. g � 10 � 3g 12. 2p � 4q � 20

13. 4(a � b) � 9a 14. 8 � 6x � 4 � 2x

15. ( f � y) � f � 5 16. s2 � n2 � 2b

Write a problem based on the given information.

17. c � cost per pound of plain coffee beans 18. p � cost of dinnerc � 3 � cost per pound of flavored coffee beans 0.15p � cost of a 15% tip2c � (c � 3) � 21 p � 0.15p � 23

1�2



1. Fifty-three plus four times c is as much as 21.

2. The sum of five times h and twice g is equal to 23.

3. One fourth the sum of r and ten is identical to r minus 4.

4. Three plus the sum of the squares of w and x is 32.

Translate each sentence into a formula.

5. Degrees Kelvin K equals 273 plus degrees Celsius C.

6. The total cost C of gas is the price p per gallon times the number of gallons g.

7. The sum S of the measures of the angles of a polygon is equal to 180 times the differenceof the number of sides n and 2.


8. q � (4 � p) � q 9. t � 2 � t

10. 9(y2 � x) � 18 11. 2(m � n) � v � 7

Write a problem based on the given information.

12. a � cost of one adult’s ticket to zoo 13. c � regular cost of one airline ticketa � 4 � cost of one children’s ticket to zoo 0.20c � amount of 20% promotional discount2a � 4(a � 4) � 38 3(c � 0.20c) � 330

14. GEOGRAPHY About 15% of all federally-owned land in the 48 contiguous states of theUnited States is in Nevada. If F represents the area of federally-owned land in thesestates, and N represents the portion in Nevada, write an equation for this situation.

FITNESS For Exercises 15–17, use the following information.Deanna and Pietra each go for walks around a lake a few times per week. Last week,Deanna walked 7 miles more than Pietra.

15. If p represents the number of miles Pietra walked, write an equation that represents thetotal number of miles T the two girls walked.

16. If Pietra walked 9 miles during the week, how many miles did Deanna walk?

17. If Pietra walked 11 miles during the week, how many miles did the two girls walktogether?

3�5

1�3

Practice Writing Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1

Reading to Learn MathematicsWriting Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1


Less

on

3-1

Pre-Activity How are equations used to describe heights?

Read the introduction to Lesson 3-1 at the top of page 120 in your textbook.

Does the equation 305 � s � 154 also represent the situation? Explain.

Reading the Lesson

1. Translate each sentence into an equation.

a. Two times the sum of x and three minus four equals four times x.

b. The difference of k and 3 is two times k divided by five.

2. A 1 oz serving of chips has 140 calories. There are about 14 servings of chips in a bag.How many calories are there in a bag of chips? Write what your solution would be as youuse each step in the Four-Step Problem-Solving Plan.

Explore What do you know?

What do you want to know?

Plan Write an equation.

Solve Solve the problem.

Examine Does your answer make sense?

Helping You Remember

3. If you cannot remember all the steps of the Four-Step Problem-Solving Plan, try toremember the first letters of the first word in each step. Write those letters here withtheir associated words.


Rep-TilesA rep-tile is a figure that can be subdivided into smaller copies of itself. The large figure is similar to the small ones and the small figures are allcongruent.

Show that each figure is a rep-tile by subdividing it into four smaller and similar figures.

1. 2. 3.

4. 5. 6.

Subdivide each rep-tile into nine smaller and similar figures.

7. 8.

9. 10.

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

3-13-1

Study Guide and InterventionSolving Equations by Using Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

3-23-2


Less

on

3-2

Solve Using Addition If the same number is added to each side of an equation, theresulting equation is equivalent to the original one. In general if the original equationinvolves subtraction, this property will help you solve the equation.

Addition Property of Equality For any numbers a, b, and c, if a � b, then a � c � b � c.

Solve m � 32 � 18.

m � 32 � 18 Original equation

m � 32 � 32 � 18 � 32 Add 32 to each side.

m � 50 Simplify.

The solution is 50.

Solve �18 � p �12.

�18 � p �12 Original equation

�18 � 12 � p �12 � 12 Add 12 to each side.

p � �6 Simplify.

The solution is �6.


ExercisesExercises

Solve each equation. Then check your solution.

1. h � 3 � �2 2. m � 8 � �12 3. p � 5 � 15

4. 20 � y � 8 5. k � 0.5 � 2.3 6. w � �

7. h � 18 � �17 8. �12 � �24 � k 9. j � 0.2 � 1.8

10. b � 40 � �40 11. m � (�12) � 10 12. w � �

Write an equation for each problem. Then solve the equation and check thesolution.

13. Twelve subtracted from a number equals 25. Find the number.

14. What number decreased by 52 equals �12?

15. Fifty subtracted from a number equals eighty. Find the number.

16. What number minus one-half is equal to negative one-half ?

17. The difference of a number and eight is equal to 14. What is the number?

18. A number decreased by fourteen is equal to eighteen. What is the number?

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3�2

5�8

1�2


Solve Using Subtraction If the same number is subtracted from each side of anequation, the resulting equation is equivalent to the original one. In general if the originalequation involves addition, this property will help you solve the equation.

Subtraction Property of Equality For any numbers a, b, and c, if a � b, then a � c � b � c.

Solve 22 � p � �12.

22 � p � �12 Original equation

22 � p � 22 � �12 � 22 Subtract 22 from each side.

p � �34 Simplify.



1. x � 12 � 6 2. z � 2 � �13 3. �17 � b � 4

4. s � (�9) � 7 5. �3.2 � � � (�0.2) 6. � � x �

7. 19 � h � �4 8. �12 � k � 24 9. j � 1.2 � 2.8

10. b � 80 � �80 11. m � (�8) � 2 12. w � �

Write an equation for each problem. Then solve the equation and check thesolution.

13. Twelve added to a number equals 18. Find the number.

14. What number increased by 20 equals �10?

15. The sum of a number and fifty equals eighty. Find the number.

16. What number plus one-half is equal to four?

17. The sum of a number and 3 is equal to �15. What is the number?

5�8

3�2

5�8

3�8


Solving Equations by Using Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

3-23-2

ExampleExample

ExercisesExercises

Skills PracticeSolving Equations by Using Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

3-23-2


Less

on

3-2


1. y � 7 � 8 2. w � 14 � �8

3. p � 4 � 6 4. �13 � 5 � x

5. 98 � b � 34 6. y � 32 � �1

7. s � (�28) � 0 8. y � (�10) � 6

9. �1 � s � (�19) 10. j � (�17) � 36

11. 14 � d � (�10) 12. u � (�5) � �15

13. 11 � �16 � y 14. c � (�3) � 100

15. 47 � w � (�8) 16. x � (�74) � �22

17. 4 � (�h) � 68 18. �56 � 20 � (�e)

Write an equation for each problem. Then solve the equation and check yoursolution.

19. A number decreased by 14 is �46. Find the number.

20. Thirteen subtracted from a number is �5. Find the number.

21. The sum of a number and 67 is equal to �34. Find the number.

22. What number minus 28 equals �2?

23. A number plus �73 is equal to 27. What is the number?

24. A number plus �17 equals �1. Find the number.

25. What number less 5 is equal to �39?



1. d � 8 � 17 2. v � 12 � �5 3. b � 2 � �11

4. �16 � s � 71 5. 29 � a � 76 6. �14 � y � �2

7. 8 � (�c) � 1 8. 78 � r � �15 9. f � (�3) � �9

10. 4.2 � n � 7.3 11. w � 1.9 � �2.5 12. 4.6 � (�b) � �0.4

13. y � (�1.5) � 0.5 14. a � 0.13 � �0.58 15. k � (�4.21) � �19

16. r � � 17. � q � 18. � h �

19. � x � � 20. y � � 21. � � (�n) � �

Write an equation for each problem. Then solve the equation and check yoursolution.

22. What number minus 9 is equal to �18?

23. A number plus 15 equals �12. What is the number?

24. The sum of a number and �3 is equal to �91. Find the number.

25. Negative seventeen equals 63 plus a number. What is the number?

26. The sum of negative 14, a number, and 6 is �5. What is the number?

27. What number plus one half is equal to three eighths?

HISTORY For Exercises 28 and 29, use the following information.

Galileo Galilei was born in 1564. Many years later, in 1642, Sir Isaac Newton was born.

28. Write an addition equation to represent the situation.

29. How many years after Galileo was born was Isaac Newton born?

HURRICANES For Exercises 30 and 31, use the following information.

The day after a hurricane, the barometric pressure in a coastal town has risen to 29.7 inches of mercury, which is 2.9 inches of mercury higher than the pressure when theeye of the hurricane passed over.

30. Write an addition equation to represent the situation.

31. What was the barometric pressure when the eye passed over?

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3�4

4�5

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2�5

1�3

2�3

5�9

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Practice Solving Equations by Using Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

3-23-2

Reading to Learn MathematicsSolving Equations by Using Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

3-23-2


Less

on

3-2

Pre-Activity How can equations be used to compare data?


In the equation m � 66 � 5, the number 5 represents

and the number 66 represents

Reading the Lesson

1. To solve x � 17 � 46 using the Subtraction Property of Equality, you would subtract from each side.

2. To solve y � 9 � �30 using the Addition Property of Equality, you would add to each side.

3. Write an equation that you could solve by subtracting 32 from each side.

4. A student used the Subtraction Property of Equality to solve an equation. Explain why itwould also be possible to use the Addition Property of Equality to solve the equation.


5. Explain how you decide whether to use the Addition Property or the SubtractionProperty of Equality to solve an equation.


Counting-Off Puzzles

Solve each puzzle.

1. Twenty-five people are standing in a circle.Starting with person 1, they count off from 1 to 7 and then start over with 1. Each person who says “7” drops out of the circle.Who is the last person left?

2. Forty people stand in a circle. They count off so that every third person drops out. Which two people are the last ones left?

3. Only half of the 30 students in Sharon’s class can go on a field trip. Sharon arranges the boys and girls as shown. They count off from 1 to 9 and every ninthperson drops out until only 15 people are left. Who gets to go on the field trip.

A group of people stand in a circle and count off 1, 2, 1, 2, 1 and so on. Every second person drops out. Person number 1 is the last person left.

4. Draw a diagram to show why the number of people in the circle must be even. Then, explain your answer.

5. When the count returns to person number 1 for the first time, how many people have dropped out?

6. Find the number of people in the circle if the number is between 10 and 20. Do the same if the number is between 30 and 40. What can you conclude about the original number of people?

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Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

3-23-2

Study Guide and InterventionSolving Equations by Using Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

3-33-3


Less

on

3-3

Solve Using Multiplication If each side of an equation is multiplied by the samenumber, the resulting equation is equivalent to the given one. You can use the property tosolve equations involving multiplication and division.

Multiplication Property of Equality For any numbers a, b, and c, if a � b, then ac � bc.

Solve 3 p � 1 .

3 p � 1 Original equation

p � Rewrite each mixed number as animproper fraction.

� p� � � � Multiply each side by .

p � Simplify.

The solution is .3�7

3�7

2�7

3�2

2�7

7�2

2�7

3�2

7�2

1�2

1�2

1�2

1�2

Solve � n � 16.

� n � 16 Original equation

�4�� n� � �4(16) Multiply each side by �4.

n � �64 Simplify.


1�4

1�4

1�4


ExercisesExercises


1. � �2 2. m � 6 3. p �

4. 5 � 5. � k � �2.5 6. � �

7. �1 h � 4 8. �12 � � k 9. �

10. �3 b � 5 11. m � 10 12. � �

Write an equation for each problem. Then solve the equation.

13. One-fifth of a number equals 25. Find the number.

14. What number divided by 2 equals �18?

15. A number divided by eight equals 3. Find the number.

16. One and a half times a number equals 6. Find the number.

1�4

p�5

7�10

1�3

2�5

j�3

3�2

1�2

5�8

m�8

1�4

y�12

3�5

1�5

1�8

h�3


Solve Using Division To solve equations with multiplication and division, you can alsouse the Division Property of Equality. If each side of an equation is divided by the samenumber, the resulting equation is true.

Division Property of Equality For any numbers a, b, and c, with c � 0, if a � b, then � .b�c

a�c


Solving Equations by Using Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

3-33-3

Solve 8n � 64.

8n � 64 Original equation

� Divide each side by 8.

n � 8 Simplify.

The solution is 8.

64�8

8n�8

Solve �5n � 60.

�5n � 60 Original equation

� Divide each side by �5.

n � �12 Simplify.


60��5

�5n��5


ExercisesExercises


1. 3h � �42 2. 8m � 16 3. �3t � 51

4. �3r � �24 5. 8k � �64 6. �2m � 16

7. 12h � 4 8. �2.4p � 7.2 9. 0.5j � 5

10. �25 � 5m 11. 6m � 15 12. �1.5p � �75


13. Four times a number equals 64. Find the number.

14. What number multiplied by �4 equals �16?

15. A number times eight equals �36. Find the number.

Skills PracticeSolving Equations by Using Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

3-33-3


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1. 12z � 108 2. �7t � 49

3. 18e � �216 4. �22 � 11v

5. �6d � �42 6. 96 � �24a

7. � 16 8. � 9

9. �84 � 10. � � �13

11. � �13 12. 31 � � n

13. �6 � z 14. q � �4

15. p � �10 16. �

17. �0.4b � 5.2 18. 1.6m � �4


19. The opposite of a number is �9. What is the number?

20. Fourteen times a number is �42. Find the number.

21. Eight times a number equals 128. What is the number?

22. Negative twelve times a number equals �132. Find the number.

23. Negative eighteen times a number is �54. What is the number?

24. One sixth of a number is �17. Find the number.

25. Negative three fifths of a number is �15. What is the number?

2�5

a�10

5�9

2�7

2�3

1�6

t�4

d�7

d�3

a�16

c�4



1. 8j � 96 2. �13z � �39 3. �180 � 15m

4. 243 � 27c 5. � �8 6. � � �8

7. � 8. � 9. �

10. �1 � � t 11. � w � �9 12. � s � 4

13. �3x � 14. a � 15. h �

16. 5n � 17. 2.5k � 20 18. �3.4e � �3.74

19. �1.7b � 2.21 20. 0.26p � 0.104 21. 4.2q � �3.36


22. Negative nine times a number equals �117. Find the number.

23. Negative one eighth of a number is � . What is the number?

24. Five sixths of a number is � . Find the number.

25. 2.7 times a number equals 8.37. What is the number?

26. One and one fourth times a number is one and one third. What is the number?

27. PUBLISHING Two units of measure used in publishing are the pica and the point. A picais one sixth of an inch. There are 12 points in a pica, so Points � 12 · Picas. How manypicas are equivalent to 108 points?

ROLLER COASTERS For Exercises 28 and 29, use the following information.

Superman the Escape in California is the fastest roller coaster in the world. Riders fall 415 feet in 7 seconds. Speeds reach a maximum of 100 miles per hour.

28. If x represents the average rate of fall of the roller coaster, write an expression torepresent the situation (Hint: Use the distance formula d � rt.)

29. What is the average rate that riders fall in feet per second?

5�9

3�4

11�4

11�6

5�3

4�3

8�5

3�2

3�15

3�8

4�7

1�6

q�24

2�9

g�27

4�5

a�15

j�12

y�9

Practice Solving Equations by Using Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

3-33-3

Reading to Learn MathematicsSolving Equations by Using Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

3-33-3


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Pre-Activity How can equations be used to find how long it takes light to reachEarth?


• In the equation d � rt, shown in the introduction, what number is usedfor r? for d?

• What equation could you use to find the time it takes light to reach Earthfrom the farthest star in the Big Dipper?

Reading the Lesson

Complete the sentence after each equation to tell how you would solve theequation.

1. � 16 each side by .

2. 5x � 125 each side by , or multiply each side by .

3. �8k � 96 Divide each side by , or multiply each side by

4. Explain how rewriting 4 x � 2 as x � helps you solve the equation.


5. One way to remember something is to explain it to someone else. Write how you would

explain to a classmate how to solve the equation x � 12.2�3

17�8

13�3

1�8

1�3

x�7


Dissection Puzzles: Make the SquareIn a dissection puzzle, you are to cut apart one figure using onlystraight cuts and then rearrange the pieces to make a new figure.Usually the puzzle-solver must figure out where to make the givennumber of cuts. However, for these puzzles, the cut lines are shown.You must discover how to rearrange the pieces.

Cut apart each figure. Then rearrange the pieces to form a square.

1.

2.

3.

4. Hint: Cut one of the triangles into two pieces to make this square.

A AA A

A

2x 2x 2x

x

A AA A

B

2x 2x x

x

A

C

B

D

A

BB

BB

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

3-33-3

Study Guide and InterventionSolving Multi-Step Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-43-4


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Work Backward Working backward is one of many problem-solving strategies thatyou can use to solve problems. To work backward, start with the result given at the end of aproblem and undo each step to arrive at the beginning number.

A number is dividedby 2, and then 8 is subtracted fromthe quotient. The result is 16. Whatis the number?

Solve the problem by working backward.The final number is 16. Undosubtracting 8 by adding 8 to get 24. Toundo dividing 24 by 2, multiply 24 by 2to get 48.The original number is 48.

A bacteria culture doubleseach half hour. After 3 hours, there are6400 bacteria. How many bacteria werethere to begin with?

Solve the problem by working backward.The bacteria have grown for 3 hours. Since thereare 2 one-half hour periods in one hour, in 3 hoursthere are 6 one-half hour periods. Since thebacteria culture has grown for 6 time periods, ithas doubled 6 times. Undo the doubling byhalving the number of bacteria 6 times.

6,400 � � � � � � � 6,400 �

� 100

There were 100 bacteria to begin with.

1�64

1�2

1�2

1�2

1�2

1�2

1�2


ExercisesExercises

Solve each problem by working backward.

1. A number is divided by 3, and then 4 is added to the quotient. The result is 8. Find thenumber.

2. A number is multiplied by 5, and then 3 is subtracted from the product. The result is 12.Find the number.

3. Eight is subtracted from a number, and then the difference is multiplied by 2. The resultis 24. Find the number.

4. Three times a number plus 3 is 24. Find the number.

5. CAR RENTAL Angela rented a car for $29.99 a day plus a one-time insurance cost of$5.00. Her bill was $124.96. For how many days did she rent the car?

6. MONEY Mike withdrew an amount of money from his bank account. He spent onefourth for gasoline and had $90 left. How much money did he withdraw?

7. TELEVISIONS In 1999, 68% of households with TV’s subscribed to cable TV. If 8,000 moresubscribers are added to the number of households with cable, the total number ofhouseholds with cable TV would be 67,600,000. How many households were there withTV in 1999? Source: World Almanac


Solve Multi-Step Equations To solve equations with more than one operation, oftencalled multi-step equations, undo operations by working backward. Reverse the usualorder of operations as you work.

Solve 5x � 3 � 23.

5x � 3 � 23 Original equation.

5x � 3 � 3 � 23 � 3 Subtract 3 from each side.

5x � 20 Simplify.


x � 4 Simplify.


1. 5x � 2 � 27 2. 6x � 9 � 27 3. 5x � 16 � 51

4. 14n � 8 � 34 5. 0.6x � 1.5 � 1.8 6. p � 4 � 10

7. 16 � 8. 8 � � 13 9. � 3 � �13

10. � 10 11. 0.2x � 8 � �2 12. 3.2y � 1.8 � 3

13. �4 � 14. 8 � �12 � 15. 0 � 10y � 40

Write an equation and solve each problem.

16. Find three consecutive integers whose sum is 96.

17. Find two consecutive odd integers whose sum is 176.

18. Find three consecutive integers whose sum is �93.

k��4

7x � (�1)��

�8

4b � 8�

�2

g��5

3n�12

d � 12�14

7�8

20�5

5x�5


Solving Multi-Step Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-43-4

ExampleExample

ExercisesExercises

Skills PracticeSolving Multi-Step Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-43-4


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1. A number is divided by 2, and then the quotient is added to 8. The result is 33. Find thenumber.

2. Two is subtracted from a number, and then the difference is divided by 3. The result is30. Find the number.

3. A number is multiplied by 2, and then the product is added to 9. The result is 49. Whatis the number?

4. ALLOWANCE After Ricardo received his allowance for the week, he went to the mallwith some friends. He spent half of his allowance on a new paperback book. Then hebought himself a snack for $1.25. When he arrived home, he had $5.00 left. How muchwas his allowance?


5. 5x � 3 � 23 6. 4 � 3a � 14 7. 2y � 5 � 19

8. 6 � 5c � �29 9. 8 � 5w � �37 10. 18 � 4v � 42

11. � 8 � �2 12. 5 � � 1 13. � � 4 � 13

14. � � 12 � �7 15. � 2 � 9 16. � 3 � �1

17. q � 7 � 8 18. g � 6 � �12 19. z � 8 � �3

20. m � 2 � 6 21. � 3 22. � 2


23. Twice a number plus four equals 6. What is the number?

24. Sixteen is seven plus three times a number. Find the number.

25. Find two consecutive integers whose sum is 35.

26. Find three consecutive integers whose sum is 36.

b � 1�3

c � 5�4

4�5

5�2

2�3

3�4

w�7

a�5

d�6

h�3

x�4

n�3



1. Three is added to a number, and then the sum is multiplied by 4. The result is 16. Findthe number.

2. A number is divided by 4, and the quotient is added to 3. The result is 24. What is thenumber?

3. Two is subtracted from a number, and then the difference is multiplied by 5. The resultis 30. Find the number.

4. BIRD WATCHING While Michelle sat observing birds at a bird feeder, one fourth of thebirds flew away when they were startled by a noise. Two birds left the feeder to go toanother stationed a few feet away. Three more birds flew into the branches of a nearbytree. Four birds remained at the feeder. How many birds were at the feeder initially?


5. �12n � 19 � 77 6. 17 � 3f � 14 7. 15t � 4 � 49

8. � 6 � 2 9. � 3 � 15 10. � 6 � �2

11. y � � 12. �32 � f � �17 13. 8 � k � �4

14. � 1 15. � �9 16. � 16

17. � 0.5 � 2.5 18. 2.5g � 0.45 � 0.95 19. 0.4m � 0.7 � 0.22


20. Seven less than four times a number equals 13. What is the number?

21. Find two consecutive odd integers whose sum is 116.

22. Find two consecutive even integers whose sum is 126.

23. Find three consecutive odd integers whose sum is 117.

24. COIN COLLECTING Jung has a total of 92 coins in his coin collection. This is 8 morethan three times the number of quarters in the collection. How many quarters does Junghave in his collection?

x�7

3k � 7�5

15 � a�3

r � 13�12

3�8

3�5

7�8

1�8

1�2

b�3

d��4

u�5

Practice Solving Multi-Step Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-43-4

Reading to Learn MathematicsSolving Multi-Step Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

3-43-4


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on

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Pre-Activity How can equations be used to estimate the age of an animal?


• Write the equation 8 � 12a � 124 in words.

• How many operations are involved in the equation?

Reading the Lesson

1. What does the phrase undo the operations mean to you? Give an example.

2. a. If we undo operations in reverse of the order of operations, what operations do we dofirst?

b. What operations do we do last?

3. Suppose you want to solve � 6.

a. What is the grouping symbol in the equation � 6?

b. What is the first step in solving the equation?

c. What is the next step in solving the equation?

4. Write an equation for the problem below.

Seven times k minus five equals negative forty-seven


5. Explain why working backward is a useful strategy for solving equations.

x � 3�5

x � 3�5


Consecutive Integer ProblemsMany types of problems and puzzles involve the idea of consecutiveintegers. Knowing how to represent these integers algebraically canhelp to solve the problem.

Find four consecutive odd integers whose sum is �80.

An odd integer can be written as 2n � 1, where n is any integer.If 2n + 1 is the first odd integer, then add 2 to get the next largest oddinteger, and so on.Now write an equation to solve this problem.(2n � 1) � (2n � 3) � (2n � 5) � (2n � 7) � �80

Write an equation for each problem. Then solve.

1. Complete the solution to the problem in the example.

2. Find three consecutive even integers whose sum is 132.



5. The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.

6. The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.

7. Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.

8. Find a set of four consecutive positive integers such that the greatest integer in the set is twice the least integer in the set.

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

3-43-4

ExampleExample

ExercisesExercises

Study Guide and InterventionSolving Equations with the Variable on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

3-53-5


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3-5

Variables on Each Side To solve an equation with the same variable on each side,first use the Addition or the Subtraction Property of Equality to write an equivalentequation that has the variable on just one side of the equation. Then solve the equation.

Solve 5y � 8 � 3y � 12.

5y � 8 � 3y � 125y � 8 � 3y � 3y � 12 � 3y

2y � 8 � 122y � 8 � 8 � 12 � 8

2y � 20

�

y � 10

The solution is 10.

20�2

2y�2

Solve �11 � 3y � 8y � 1.

�11 � 3y � 8y � 1�11 � 3y � 3y � 8y � 1 � 3y

�11 � 11y � 1�11 � 1 � 11y � 1 � 1

�12 � 11y

�

�1 � y

The solution is �1 .1�11

1�11

11y�11

�12�11


ExercisesExercises


1. 6 � b � 5b � 30 2. 5y � 2y � 3y � 2 3. 5x � 2 � 2x � 10

4. 4n � 8 � 3n � 2 5. 1.2x � 4.3 � 2.1 � x 6. 4.4s � 6.2 � 8.8s � 1.8

7. b � 4 � b � 88 8. k � 5 � k � 1 9. 8 � 5p � 4p � 1

10. 4b � 8 � 10 � 2b 11. 0.2x � 8 � �2 � x 12. 3y � 1.8 � 3y � 1.8

13. �4 � 3x � 7x � 6 14. 8 � 4k � �10 � k 15. 20 � a � 10a � 2

16. n � 8 � n � 2 17. y � 8 � 9 � y 18. �4r � 5 � 5 � 4r

19. �4 � 3x � 6x � 6 20. 18 � 4k � �10 �4k 21. 12 � 2y � 10y � 12

3�5

2�5

1�2

2�3

1�4

3�4

1�8

1�2


Grouping Symbols When solving equations that contain grouping symbols, first usethe Distributive Property to eliminate grouping symbols. Then solve.

Solve 4(2a � 1) � �10(a � 5).

4(2a � 1) � �10(a � 5) Original equation

8a � 4 � �10a � 50 Distributive Property

8a � 4 � 10a � �10a � 50 � 10a Add 10a to each side.

18a � 4 � 50 Simplify.

18a � 4 � 4 � 50 � 4 Add 4 to each side.

18a � 54 Simplify.


a � 3 Simplify.

The solution is 3.


1. �3(x � 5) � 3(x � 1) 2. 2(7 � 3t) � �t 3. 3(a � 1) � 5 � 3a � 2

4. 75 � 9g � 5(�4 � 2g) 5. 5(f � 2) � 2(3 � f ) 6. 4(p � 3) � 36

7. 18 � 3(2c � 2) 8. 3(d � 8) � 3d 9. 5(p � 3) � 9 � 3(p � 2) � 6

10. 4(b � 2) � 2(5 � b) 11. 1.2(x � 2) � 2 � x 12. �

13. � 14. 2(4 � 2k) � 10 � k 15. 2(w � 1) � 4 � 4(w � 1)

16. 6(n � 1) � 2(2n � 4) 17. 2[2 � 3( y � 1)] � 22 18. �4(r � 2) � 4(2 � 4r)

19. �3(x � 8) � 24 20. 4(4 � 4k) � �10 �16k 21. 6(2 � 2y) � 5(2y � 2)

2a � 5�3

a � 8�12

�y �8

3 � y�4

54�18

18a�18


Solving Equations with the Variable on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

3-53-5

ExampleExample

ExercisesExercises

Skills PracticeSolving Equations with the Variable on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

3-53-5


Less

on

3-5

Justify each step.

1. 4k � 3 � 2k � 54k � 3 � 2k � 2k � 5 � 2k a.

2k � 3 � 5 b.

2k � 3 � 3 � 5 � 3 c.

2k � 8 d.

� e.

k � 4 f.

2. 2(8u � 2) � 3(2u � 7)16u � 4 � 6u � 21 a.

16u � 4 � 6u � 6u � 21 � 6u b.

10u � 4 � �21 c.

10u � 4 � 4 � �21 � 4 d.

10u � �25 e.

� f.

u � �2.5 g.


3. 2m � 12 � 3m � 31 4. 2h � 8 � h � 17

5. 7a � 3 � 3 � 2a 6. 4n � 12 � 12 � 4n

7. 4x � 9 � 7x � 12 8. �6y � 3 � 3 � 6y

9. 5 � 3r � 5r � 19 10. �9 � 8k � 7 � 4k

11. 8q � 12 � 4(3 � 2q) 12. 3(5j � 2) � 2(3j � 6)

13. 6(�3v � 1) � 5(�2v � 2) 14. �7(2b � 4) � 5(�2b � 6)

15. 3(8 � 3t) � 5(2 � t) 16. 2(3u � 7) � �4(3 � 2u)

17. 8(2f � 2) � 7(3f � 2) 18. 5(�6 � 3d) � 3(8 � 7d)

19. 6(w � 1) � 3(3w � 5) 20. 7(�3y � 2) � 8(3y � 2)

21. v � 6 � 6 � v 22. � x � x �7�2

7�8

5�8

1�2

2�3

2�3

�25�10

10u�10

8�2

2k�2



1. 5x � 3 � 13 � 3x 2. �4c � 11 � 4c � 21

3. 1 � s � 6 � 6s 4. 14 � 5n � �4n � 17

5. k � 3 � 2 � k 6. (6 � z) � z

7. 3(�2 � 3x) � �9x � 4 8. 4(4 � w) � 3(2w � 2)

9. 9(4b � 1) � 2(9b � 3) 10. 3(6 � 5y) � 2(�5 � 4y)

11. �5x � 10 � 2 � (x � 4) 12. 6 � 2(3j � 2) � 4(1 � j)

13. t � t � 3 � t 14. 1.4f � 1.1 � 8.3 � f

15. x � � x � 16. 2 � z � z � 9

17. (3g � 2) � 18. (c � 1) � (3c � 5)

19. (5 � 2h) � 20. (2m � 16) � (2m � 4)

21. 3(d � 8) � 5 � 9(d � 2) � 1 22. 2(a � 8) � 7 � 5(a � 2) � 3a � 19

23. Two thirds of a number reduced by 11 is equal to 4 more than the number. Find thenumber.

24. Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twicethe number. What is the number?

25. NUMBER THEORY Tripling the greater of two consecutive even integers gives the sameresult as subtracting 10 from the lesser even integer. What are the integers?

26. GEOMETRY The formula for the perimeter of a rectangle is P � 2� � 2w, where � isthe length and w is the width. A rectangle has a perimeter of 24 inches. Find itsdimensions if its length is 3 inches greater than its width.

1�3

1�9

h�2

1�4

1�6

1�3

g�6

1�2

1�8

3�4

5�6

1�2

1�6

2�3

3�2

5�2

1�2

3�4

1�2

Practice Solving Equations with the Variable on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

3-53-5

Reading to Learn MathematicsSolving Equations with the Variable on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

3-53-5


Less

on

3-5

Pre-Activity How can an equation be used to determine when two populationsare equal?


In the equation 12 � 7.6x � 6 � 8x, what do 7.6x and 8x represent?

Reading the Lesson

1. Suppose you want to help a friend solve 6k � 7 � 3k � 8. What would you advise her todo first? Why?

2. When solving 2(3x � 4)� 3(x � 5), why is it helpful first to use the Distributive Propertyto remove the grouping symbols?

3. On a quiz, Jason solved three equations. His teacher said all the work was correct, butshe asked him to write short sentences to tell what the solutions were. In what follows,you see the last equation in his work for each equation. Write sentences to describe thesolutions.

a. x � �4

b. 6m � 6m

c. 12 � 37

4. In Question 3, one of the equations Jason solved was an identity. Which equation was it?Explain how you know.


5. An equation with variables is an identity when the equation is always true. In otherwords, the expressions on the left and right sides always have the same value. Look upthe word identity in the dictionary. Write all the definitions that are similar to themathematical definition.


IdentitiesAn equation that is true for every value of the variable is called anidentity. When you try to solve an identity, you end up with astatement that is always true. Here is an example.

Solve 8 � (5 � 6x) � 3(1 � 2x).

8 � (5 � 6x) � 3(1 � 2x)

8 � 5 � (�6x) � 3(1 � 2x)

8 � 5 � 6x � 3 � 6x

3 � 6x � 3 � 6x

State whether each equation is an identity. If it is not, find its solution.

1. 2(2 � 3x) � 3(3 � x) � 4 2. 5(m � 1) � 6 � 3(4 � m) � (2m � 1)

3. (5t � 9) � (3t � 13) � 2(11 � t) 4. 14 � (6 � 3c) � 4c � c

5. 3y � 2( y � 19) � 9y � 3(9 � y) 6. 3(3h � 1) � 4(h � 3)

7. Use the true equation 3x � 2 � 3x � 2 to create an identity of your own.

8. Use the false equation 1 � 2 to create an equation with no solution.

9. Create an equation whose solution is x � 3.

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

3-53-5

ExampleExample

ExercisesExercises

Study Guide and InterventionRatios and Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

3-63-6


Less

on

3-6

Ratios and Proportions A ratio is a comparison of two numbers by division. The ratio

of x to y can be expressed as x to y, x:y or . Ratios are usually expressed in simplest form.

An equation stating that two ratios are equal is called a proportion. To determine whethertwo ratios form a proportion, express both ratios in simplest form or check cross products.

x�y

Determine whether the

ratios and form a proportion.

� when expressed in simplest form.

� when expressed in simplest form.

The ratios and form a proportion

because they are equal when expressed insimplest form.

12�18

24�36

2�3

12�18

2�3

24�36

12�18

24�36

Use cross products to

determine whether and form aproportion.

� Write the proportion.

10(45) � 18(25) Cross products

450 � 450 Simplify.

The cross products are equal, so � .

Since the ratios are equal, they form aproportion.

25�45

10�18

25�45

10�18

25�45

10�18


ExercisesExercises

Use cross products to determine whether each pair of ratios forms a proportion.

1. , 2. , 3. ,

4. , 5. , 6. ,

7. , 8. , 9. ,

10. 2:3, 20:30 11. 5 to 9, 25 to 45 12. ,

13. 5:5, 30:20 14. 18 to 24, 50 to 75 15. 100:75, 44:33

16. , 17. , 18. , 0.45�0.9

0.1�0.2

6�8

1.5�2

1�20

0.05�1

9�8

72�64

20�30

14�21

9�12

15�20

5�100

0.1�2

12�27

4�9

3�16

12�32

15�20

25�36

25�49

10�20

10�15

5�8

16�32

1�2


Solve Proportions If a proportion involves a variable, you can use cross products to solve

the proportion. In the proportion � , x and 13 are called extremes and 5 and 10 are

called means. In a proportion, the product of the extremes is equal to the product of the means.

Means-Extremes Property of Proportions For any numbers a, b, c, and d, if � , then ad � bc.

Solve � .

� Original proportion

13(x) � 5(10) Cross products

13x � 50 Simplify.


x � 3 Simplify.

The solution is 3 .

Solve each proportion.

1. � 2. � 3. �

4. � 5. � 6. �

7. � 8. � 9. �

10. � 11. � 12. �

13. � 14. � 15. �

Use a proportion to solve each problem.

16. MODELS To make a model of the Guadeloupe River bed, Hermie used 1 inch of clay for5 miles of the river’s actual length. His model river was 50 inches long. How long is theGuadeloupe River?

17. EDUCATION Josh finished 24 math problems in one hour. At that rate, how manyhours will it take him to complete 72 problems?

12�9

2 � w�6

24�k

12�k

15�3

a � 8�12

�y�8

3 � y�4

12�x

1.5�x

4�12

4�b � 2

p�24

5�8

18�3

3�d

18�54

9�y � 1

3�63

x�21

8�x

4�6

3�4

x � 1�4

0.5�x

0.1�2

5�3

1�t

2�8

�3�x

11�13

11�13

50�13

13x�13

10�13

x�5

10�13

x�5

c�d

a�b

10�13

x�5


Ratios and Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

3-63-6

ExampleExample

ExercisesExercises

Skills PracticeRatios and Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

3-63-6


Less

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3-6

Use cross products to determine whether each pair of ratios forms a proportion.Write yes or no.

1. , 2. ,

3. , 4. ,

5. , 6. ,

7. , 8. ,

Solve each proportion. If necessary, round to the nearest hundredth.

9. � 10. �

11. � 12. �

13. � 14. �

15. � 16. �

17. � 18. �

19. � 20. �

21. � 22. �

23. � 24. �

25. BOATING Hue’s boat used 5 gallons of gasoline in 4 hours. At this rate, how manygallons of gasoline will the boat use in 10 hours?

11�30

22�x

s�84

4�21

20�g

5�12

27�39

9�c

n�60

11�15

30�m

10�14

1�9

7�b

6�f

42�56

y�69

6�23

36�s

12�7

35�21

5�e

3�5

6�z

1�6

3�a

15�10

9�g

3�9

5�b

2�14

1�a

50�85

12�17

21�98

3�14

26�38

13�19

42�90

7�16

72�81

8�9

24�28

6�7

7�11

5�9

20�25

4�5


Use cross products to determine whether each pair of ratios forms a proportion.Write yes or no.

1. , 2. , 3. ,

4. , 5. , 6. ,

7. , 8. , 9. ,

Solve each proportion. If necessary, round to the nearest hundredth.

10. � 11. � 12. �

13. � 14. � 15. �

16. � 17. � 18. �

19. � 20. � 21. �

22. � 23. � 24. �

25. � 26. � 27. �

28. � 29. � 30. �

31. � 32. � 33. �

34. PAINTING Ysidra paints a room that has 400 square feet of wall space in 2 hours. At

this rate, how long will it take her to paint a room that has 720 square feet of wallspace?

35. VACATION PLANS Walker is planning a summer vacation. He wants to visit PetrifiedNational Forest and Meteor Crater, Arizona, the 50,000-year-old impact site of a largemeteor. On a map with a scale where 2 inches equals 75 miles, the two areas are about

1 inches apart. What is the distance between Petrified National Forest and Meteor

Crater?

1�2

1�2

x � 2�6

3�7

5�7

r � 2�7

x � 1�4

5�12

2�4

m � 1�8

2�y � 6

3�12

14�6

7�a � 4

3�0.51

6�n

12�b

3�0.72

7�1.61

v�0.23

5�8

m�6

5�6

3�q

8�c

7�9

2�a

14�49

6�4

g�16

12�h

6�61

z�17

3�51

35�x

5�11

10�60

2�y

48�9

y�3

27�162

3�u

4�w

28�49

k�7

40�56

34�23

v�46

30�54

5�a

3.9�0.9

7.6�1.8

2.9�2.4

1.7�1.2

7.14�10.92

3.4�5.2

1�6

1.5�9

72�81

8�9

108�99

12�11

36�48

18�24

15�66

3�11

52�48

7�6

Practice Ratios and Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

3-63-6

Reading to Learn MathematicsRatios and Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

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3-6

Pre-Activity How are ratios used in recipes?


• How many servings of honey frozen yogurt are made by this recipe?

• How many recipes would be needed to make enough honey frozen yogurtfor all the students in your class?

Reading the Lesson

1. Complete the following sentence.

A ratio is a comparison of two numbers by .

2. Describe two ways to decide whether the sentence � is a proportion.

3. For each proportion, tell what the extremes are and what the means are.

a. � Extremes: Means:

b. � Extremes: Means:

4. A jet flying at a steady speed traveled 825 miles in 2 hours. If you solved the proportion

� , what would the answer tell you about the jet?


5. Write how you would explain solving a proportion to a friend who missed Lesson 3-6.

x�1.5

825�2

12�16

6�8

6�15

14�35

8�20

2�5


Angles of a TriangleIn geometry, many statements about physical space are proven to betrue. Such statements are called theorems. Here are two examples ofgeometric theorems.

a. The sum of the measures of the angles of a triangle is 180°.b. If two sides of a triangle have equal measure, then the two angles

opposite those sides also have equal measure.

For each of the triangles, write an equation and then solve for x. (A tick mark ontwo or more sides of a triangle indicates that the sides have equal measure.)

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. Two angles of a triangle have the same 12. The measure of one angle of a triangle is measure. The sum of the measures of twice the measure of a second angle. The these angles is one-half the measure of measure of the third angle is 12 less than the third angle. Find the measures of the sum of the other two. Find the the angles of the triangle. measures of the angles of the triangle.

x2x

30°

x

40°

x

x � 15°

3x

x � 30°

90°

4x

5x

5x

2x x

x � 30°

x5x � 10°

90° x

90° 45°

x70°

50°x

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

3-63-6

Study Guide and InterventionPercent of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

3-73-7


Less

on

3-7

Percent of Change When an increase or decrease in an amount is expressed as apercent, the percent is called the percent of change. If the new number is greater than theoriginal number, the percent of change is a percent of increase. If the new number is lessthan the original number, the percent of change is the percent of decrease.

Find the percent of increase.original: 48new: 60

First, subtract to find the amount ofincrease. The amount of increase is 60 � 48 � 12.Then find the percent of increase by usingthe original number, 48, as the base.

� Percent proportion

12(100) � 48(r) Cross products

1200 � 48r Simplify.


25 � r Simplify.

The percent of increase is 25%.

48r�48

1200�48

r�100

12�48

Find the percent of decrease.original: 30new: 22

First, subtract to find the amount ofdecrease. The amount of decrease is 30 � 22 � 8.Then find the percent of decrease by usingthe original number, 30, as the base.

� Percent proportion

8(100) � 30(r) Cross products

800 � 30r Simplify.


26 � r Simplify.

The percent of decrease is 26 %, or about27%.

2�3

2�3

30r�30

800�30

r�100

8�30


ExercisesExercises

State whether each percent of change is a percent of increase or a percent ofdecrease. Then find each percent of change. Round to the nearest whole percent.

1. original: 50 2. original: 90 3. original: 45new: 80 new: 100 new: 20

4. original: 77.5 5. original: 140 6. original: 135new: 62 new: 150 new: 90

7. original: 120 8. original: 90 9. original: 27.5new: 180 new: 270 new: 25

10. original: 84 11. original: 12.5 12. original: 250new: 98 new: 10 new: 500


Solve Problems Discounted prices and prices including tax are applications of percentof change. Discount is the amount by which the regular price of an item is reduced. Thus,the discounted price is an example of percent of decrease. Sales tax is amount that is addedto the cost of an item, so the price including tax is an example of percent of increase.

A coat is on sale for 25% off the original price. If the original priceof the coat is $75, what is the discounted price?

The discount is 25% of the original price.

25% of $75 � 0.25 � 75 25% � 0.25

� 18.75 Use a calculator.

Subtract $18.75 from the original price.$75 � $18.75 � $56.25

The discounted price of the coat is $56.25.

Find the final price of each item. When a discount and a sales tax are listed,compute the discount price before computing the tax.

1. Compact disc: $16 2. Two concert tickets: $28 3. Airline ticket: $248.00Discount: 15% Student discount: 28% Superair discount: 33%

4. Shirt: $24.00 5. CD player: $142.00 6. Celebrity calendar: $10.95Sales tax: 4% Sales tax: 5.5% Sales tax: 7.5%

7. Class ring: $89.00 8. Software: $44.00 9. Video recorder: $110.95Group discount: 17% Discount: 21% Discount: 20%Sales tax: 5% Sales tax: 6% Sales tax: 5%

10. VIDEOS The original selling price of a new sports video was $65.00. Due to the demandthe price was increased to $87.75. What was the percent of increase over the originalprice?

11. SCHOOL A high school paper increased its sales by 75% when it ran an issue featuringa contest to win a class party. Before the contest issue, 10% of the school’s 800 studentsbought the paper. How many students bought the contest issue?

12. BASEBALL Baseball tickets cost $15 for general admission or $20 for box seats. Thesales tax on each ticket is 8%, and the municipal tax on each ticket is an additional 10%of the base price. What is the final cost of each type of ticket?


Percent of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

3-73-7

ExampleExample

ExercisesExercises

Skills PracticePercent of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

3-73-7


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1. original: 25 2. original: 50new: 10 new: 75




Find the total price of each item.

9. dress: $69.00 10. binder: $14.50tax: 5% tax: 7%

11. hardcover book: $28.95 12. groceries: $47.52tax: 6% tax: 3%

13. filler paper: $6.00 14. shoes: $65.00tax: 6.5% tax: 4%

15. basketball: $17.00 16. concert tickets: $48.00tax: 6% tax: 7.5%

Find the discounted price of each item.

17. backpack: $56.25 18. monitor: $150.00discount: 20% discount: 50%

19. CD: $15.99 20. shirt: $25.50discount: 20% discount: 40%

21. sleeping bag: $125 22. coffee maker: $102.00discount: 25% discount: 45%





7. original: 15 8. original: 98.6 9. original: 58.8new: 35.5 new: 64 new: 65.7

Find the total price of each item.

10. concrete blocks: $95.00 11. crib: $240.00 12. jacket: $125.00tax: 6% tax: 6.5% tax: 5.5%

13. class ring: $325.00 14. blanket: $24.99 15. kite: $18.90tax: 6% tax: 7% tax: 5%

Find the discounted price of each item.

16. dry cleaning: $25.00 17. computer game: $49.99 18. luggage: $185.00discount: 15% discount: 25% discount: 30%

19. stationery: $12.95 20. prescription glasses: $149 21. pair of shorts: $24.99 discount: 10% discount: 20% discount: 45%

Find the final price of each item.

22. television: $375.00 23. DVD player: $269.00 24. printer: $255.00discount: 25% discount: 20% discount: 30%tax: 6% tax: 7% tax: 5.5%

25. INVESTMENTS The price per share of an internet-related stock decreased from $90 pershare to $36 per share early in 2001. By what percent did the price of the stockdecrease?

26. HEATING COSTS Customers of a utility company received notices in their monthly billsthat heating costs for the average customer had increased 125% over last year becauseof an unusually severe winter. In January of last year, the Garcia’s paid $120 for heating.What should they expect to pay this January if their bill increased by 125%?

Practice Percent of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

3-73-7

Reading to Learn MathematicsPercent of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

3-73-7


Less

on

3-7

Pre-Activity How can percents describe growth over time?


• How many area codes were in use in 1947?

• How many more area codes were in use in 1999?

Reading the Lesson

1. If you use (original amount) — (new amount) to find the change for a percent of change problem, then the problem involves a percent of (increase/decrease).

2. If you use (new amount) — (original amount) to find the change for a percent of change problem, then the problem involves a percent of (increase/decrease).

Complete the chart.

Original New Percent Increase or Amount Amount

Percent ProportionPercent Decrease?

3. 10 13

4. 10 7

5. 50 42

6. 50 58

7. When you find a discount price, do you add to or subtract from the original price?


8. If you remember only two things about the ratio used for finding percent of change, whatshould they be?


Using PercentUse what you have learned about percent to solve each problem.

A TV movie had a “rating” of 15 and a 25 “share.” The rating is the percentageof the nation’s total TV households that were tuned in to this show. The shareis the percentage of homes with TVs turned on that were tuned to the movie.How many TV households had their TVs turned off at this time?To find out, let T � the number of TV households

and x � the number of TV households with the TV off.Then T � x � the number of TV households with the TV on.

Since 0.15T and 0.25(T � x) both represent the number of households tunedto the movie,

0.15T � 0.25(T � x)0.15T � 0.25T � 0.25x.

Solve for x. 0.25x � 0.10T

x � � 0.40T

Forty percent of the TV households had their TVs off when the movie was aired.

Answer each question.

1. During that same week, a sports broadcast had a rating of 22.1 and a 43 share.Show that the percent of TV households with their TVs off was about 48.6%.0.221T � 0.43T � 0.43x

x �

� 0.486T2. Find the percent of TV households with their TVs turned off during a show

with a rating of 18.9 and a 29 share. 34.8%

3. Show that if T is the number of TV households, r is the rating, and s is the

share, then the number of TV households with the TV off is .Solve rT � s(T � x) for x.

4. If the fraction of TV households with no TV on is then show that the

fraction of TV households with TVs on is .

5. Find the percent of TV households with TVs on during the most watched serial program in history: the last episode of M*A*S*H, which had a 60.3 rating and a 77 share. � 78.3%

6. A local station now has a 2 share. Each share is worth $50,000 in advertising revenue per month. The station is thinking of going commercial free for the three months of summer to gain more listeners. What would its new share have to be for the last 4 months of the year to make more money for the year than it would have made had it not gone commercial free? greater than 3.5

60.3�77

r�s

s – r�s

(s � r)T�s

0.221T � 0.43T��

�0.43

0.10T�0.25

Enrichment

NAME ______________________________________________ DATE______________ PERIOD _____

3-73-7

1 � � r�s

s � r�

s

Study Guide and InterventionSolving Equations and Formulas

NAME ______________________________________________ DATE ____________ PERIOD _____

3-83-8


Less

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3-8

Solve for Variables Sometimes you may want to solve an equation such as V � �wh forone of its variables. For example, if you know the values of V, w, and h, then the equation

� � is more useful for finding the value of �. If an equation that contains more than one

variable is to be solved for a specific variable, use the properties of equality to isolate thespecified variable on one side of the equation.

V�wh

Solve 2x � 4y � 8 for y.

2x � 4y � 82x � 4y � 2x � 8 � 2x

�4y � 8 � 2x

�

y � or

The value of y is .2x � 8�4

2x � 8�4

8 � 2x�

�4

8 � 2x�

�4�4y��4

Solve 3m � n � km � 8 for m.

3m � n � km � 83m � n � km � km � 8 � km3m � n � km � � 8

3m � n � km � n � � 8 � n3m � km � �8 � nm(3 � k) � �8 � n

�

m � , or

The value of m is . Since division by 0 is

undefined, 3 � k � 0, or k � 3.

n � 8�3 � k

n � 8�3 � k

�8 � n�3 � k

�8 � n�3 � k

m(3 � k)��3 � k


ExercisesExercises

Solve each equation or formula for the variable specified.

1. ax � b � c for x 2. 15x � 1 � y for x 3. (x � f) � 2 � j for x

4. xy � z � 9 for y 5. x(4 � k) � p for k 6. 7x � 3y � m for y

7. 4(c � 3) � t for c 8. 2x � b � c for x 9. x(1 � y) � z for x

10. 16z � 4x � y for x 11. d � rt for r 12. A � for h

13. C� (F � 32) for F 14. P � 2� � 2w for w 15. A � �w for �5�9

h(a � b)��2


Use Formulas Many real-world problems require the use of formulas. Sometimes solvinga formula for a specified variable will help solve the problem.

The formula C � �d represents the circumference of a circle, or thedistance around the circle, where d is the diameter. If an airplane could fly aroundEarth at the equator without stopping, it would have traveled about 24,900 miles.Find the diameter of Earth.

C � �d Given formula

d � Solve for d.

d � Use � � 3.14.

d � 7930 Simplify.

The diameter of Earth is about 7930 miles.

1. GEOMETRY The volume of a cylinder V is given by the formula V � �r2h, where r isthe radius and h is the height.

a. Solve the formula for h.

b. Find the height of a cylinder with volume 2500� feet and radius 10 feet.

2. WATER PRESSURE The water pressure on a submerged object is given by P � 64d,where P is the pressure in pounds per square foot, and d is the depth of the object in feet.

a. Solve the formula for d.

b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.

3. GRAPHS The equation of a line containing the points (a, 0) and (0, b) is given by the

formula � � 1.

a. Solve the equation for y.

b. Suppose the line contains the points (4, 0), and (0, �2). If x � 3, find y.

4. GEOMETRY The surface area of a rectangular solid is given by the formula S � 2�w � 2�h � 2wh, where � � length, w � width, and h � height.

a. Solve the formula for h.

b. The surface area of a rectangular solid with length 6 centimeters and width 3 centimeters is 72 square centimeters. Find the height.

y�b

x�a

24,900�3.14

C��


Solving Equations and Formulas

NAME ______________________________________________ DATE ____________ PERIOD _____

3-83-8

ExampleExample

ExercisesExercises

Skills PracticeSolving Equations and Formulas

NAME ______________________________________________ DATE ____________ PERIOD _____

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Less

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1. 7t � x, for t 2. e � wp, for p

3. q � r � r, for r 4. 4m � n � m, for m

5. 7a � b � 15a, for a 6. �5c � d � 2c, for c

7. x � 2y � 1, for y 8. m � 3n � 1, for n

9. 7f � g � 5, for f 10. ax � c � b, for x

11. rt � 2n � y, for t 12. bc � 3g � 2k, for c

13. kn � 4f � 9v, for n 14. 8c � 6j � 5p, for c

15. � d, for x 16. � d, for c

17. � q, for p 18. � a, for b

Write an equation and solve for the variable specified.

19. Five more than a number g is six less than twice a number h. Solve for g.

20. One fourth of a number q is three more than three times a number w. Solve for q.

21. Eight less than a number s is three more than four times a number t. Solve for s.

b � 4z�7

p � 9�5

x � c�2

x � c�2



1. d � rt, for r 2. 6w � y � 2z, for w

3. mx � 4y � 3c, for x 4. 9s � 5g � �4u, for s

5. ab � 3c � 2d, for b 6. 2p � kx � q, for x

7. m � a � a � c, for m 8. h � g � d, for h

9. y � v � s, for y 10. a � q � k, for a

11. � h, for x 12. � c, for b

13. 2w � y � 7w � 2, for w 14. 3� � y � 5 � 5�, for �

Write an equation and solve for the variable specified.

15. Three times a number s plus 4 times a number y is 1 more than 6 times the number s.Solve for s.

16. Five times a number k minus 9 is two thirds of a number j. Solve for j.

ELECTRICITY For Exercises 17 and 18, use the following information.

The formula for Ohm’s Law is E � IR, where E represents voltage measured in volts,I represents current measured in amperes, and R represents resistance measured in ohms.

17. Solve the formula for R.

18. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery.What is the resistance in the circuit?

MOTION For Exercises 19 and 20, use the following information.

In uniform circular motion, the speed v of a point on the edge of a spinning disk is v � r,

where r is the radius of the disk and T is the time it takes the point to travel once aroundthe circle.

19. Solve the formula for r.

20. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outsideedge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for �.)

2��T

3b � 4�2

rx � 9�5

3�4

2�3

2�5

2�3

Practice Solving Equations and Formulas

NAME ______________________________________________ DATE ____________ PERIOD _____

3-83-8

Reading to Learn MathematicsSolving Equations and Formulas

NAME ______________________________________________ DATE______________ PERIOD _____

3-83-8


Less

on

3-8

Pre-Activity How are equations used to design roller coasters?


The equation g(195 � h) � v2 contains several variables. What

number values do you know for these variables in this situation?

32 for g and 49 for v

Reading the Lesson

1. Suppose you have an equation with several variables. You want to solve for a particularvariable. How does the procedure compare with that for solving an equation with justone variable? How does the solution compare with the solution for an equation with onevariable?

Sample answer: The procedure is basically the same. You use propertiesof operations and equality to isolate the variable in which you areinterested. The solution will probably contain variables instead of just anumber.

2. Describe what dimensional analysis involves.

Sample answer: You use the units along with number values as you docalculations. You treat the units pretty much the same way you wouldvariables. For example, you can divide them and use exponents with them.

3. What do you have to be careful about when you use variables in denominators offractions?

You have to be sure that you do not use values that would make thedenominator 0.


4. When you give the dimensions of a rectangle, you have to tell how many units long it isand how many units wide it is. How can this help you remember what dimensionalanalysis involves.

Sample answer: Keep the words dimension and unit in mind. Indimensional analysis, you include units for dimensions in calculations.

1�2


Dr. Bernardo Houssay Even though researchers have been studying the disease diabetesmellitus for hundreds of years, scientists have only recently discoveredthe cause of the disease and developed methods for reducing itsseverity. Dr. Bernardo Houssay, an Argentine physiologist, was one ofthe pioneers of this more modern research. He studied the relationshipbetween diabetes and the pituitary gland, and in 1947 became the firstLatin American to win the Nobel Prize in Medicine and Physiology.

Though there is no cure for diabetes, specific diets and exercise can helppeople control the disease. The American Diabetes Association (ADA)has helped establish flexible dietary guidelines for consumers to follow.These guidelines include some of the following general nutrition rules.

• Fat intake should be equal to or less than 30% of daily calories.

• Saturated fat intake should be equal to or less than 10% of dailycalories.

• Protein should be limited to 10% to 20% of daily calories. Personsshowing the initial signs of diabetes-induced kidney disease shouldlimit protein to 10% of daily calories.

• Cholesterol intake should be 300 milligrams or less daily.

Refer to the information above for Exercises 1–4.

1. Robert consumed 2100 calories on Tuesday. His fat intake totaled70 grams, and of that 70 grams, 14 were saturated.

a. What percentage of his calorie consumption was fat, and whatpercentage of that fat was saturated? (To find the percentage ofcalories from fat, multiply the number of fat grams by 9 beforedividing by the number of calories.) 30%; 20%

b. Did Robert stay within the recommended allowance of fats? yes

2. Anna's cholesterol intake was 330 milligrams on Sunday. By whatpercentage does she need to reduce her cholesterol consumption toremain within the guidelines? 10%

3. What number of fat grams is 30% of 240 calories? 8

4. Sharon follows a diet that provides about 50 grams of protein eachday. Sharon's doctor has just told her to reduce her daily proteinintake by 30%. About how much protein will be in her reducedprotein diet? 35 grams

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Mixture Problems

Weighted AverageThe weighted average M of a set of data is the sum of the product of each number in the set and its weight divided by the sum of all the weights.

Mixture Problems are problems where two or more parts are combined into a whole. Theyinvolve weighted averages. In a mixture problem, the weight is usually a price or a percentof something.

Delectable Cookie Company sells chocolate chip cookies for $6.95per pound and white chocolate cookies for $5.95 per pound. How many pounds ofchocolate chip cookies should be mixed with 4 pounds of white chocolate cookiesto obtain a mixture that sells for $6.75 per pound.

Let w � the number of pounds of chocolate chip cookies

Number of Pounds Price per Pound Total Price

Chocolate Chip w 6.95 6.95w

White Chocolate 4 5.95 4(5.95)

Mixture w � 4 6.75 6.75(w � 4)

Equation: 6.95w � 4(5.95) � 6.75(w � 4)Solve the equation.

6.95w � 4(5.95) � 6.75(w � 4) Original equation

6.95w � 23.80 � 6.75w � 27 Simplify.

6.95w � 23.80 � 6.75w � 6.75w � 27 � 6.75w Subtract 6.75w from each side.

0.2w � 23.80 � 27 Simplify.

0.2w � 23.80 � 23.80 � 27 � 23.80 Subtract 23.80 from each side.

0.2w � 3.2 Simplify.

w � 16 Simplify.

16 pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies.

1. SOLUTIONS How many grams of sugar must be added to 60 grams of a solution that is32% sugar to obtain a solution that is 50% sugar?

2. NUTS The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound andwalnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15pounds of pecans to make a mixture that sells for $1.75 per pound?

3. INVESTMENTS Alice Gleason invested a portion of $32,000 at 9% interest and thebalance at 11% interest. How much did she invest at each rate if her total income fromboth investments was $3,200.

4. MILK Whole milk is 4% butterfat. How much skim milk with 0% butterfat should beadded to 32 ounces of whole milk to obtain a mixture that is 2.5% butterfat?

ExampleExample

ExercisesExercises


Uniform Motion Problems Motion problems are another application of weightedaverages. Uniform motion problems are problems where an object moves at a certainspeed, or rate. Use the formula d � rt to solve these problems, where d is the distance, r isthe rate, and t is the time.

Bill Gutierrez drove at a speed of 65 miles per hour on anexpressway for 2 hours. He then drove for 1.5 hours at a speed of 45 miles perhour on a state highway. What was his average speed?

M � Definition of weighted average

� 56.4 Simplify.

Bill drove at an average speed of about 56.4 miles per hour.

1. TRAVEL Mr. Anders and Ms. Rich each drove home from a business meeting. Mr. Anderstraveled east at 100 kilometers per hour and Ms. Rich traveled west at 80 kilometers perhours. In how many hours were they 100 kilometers apart.

2. AIRPLANES An airplane flies 750 miles due west in 1 hours and 750 miles due south

in 2 hours. What is the average speed of the airplane?

3. TRACK Sprinter A runs 100 meters in 15 seconds, while sprinter B starts 1.5 secondslater and runs 100 meters in 14 seconds. If each of them runs at a constant rate, who isfurther in 10 seconds after the start of the race? Explain.

4. TRAINS An express train travels 90 kilometers per hour from Smallville to Megatown.A local train takes 2.5 hours longer to travel the same distance at 50 kilometers perhour. How far apart are Smallville and Megatown?

5. CYCLING Two cyclists begin traveling in the same direction on the same bike path. Onetravels at 15 miles per hour, and the other travels at 12 miles per hour. When will thecyclists be 10 miles apart?

6. TRAINS Two trains leave Chicago, one traveling east at 30 miles per hour and onetraveling west at 40 miles per hour. When will the trains be 210 miles apart?

1�2

65 2 � 45 1.5��2 � 1.5


Weighted Averages

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SEASONING For Exercises 1–4, use the following information.

A health food store sells seasoning blends in bulk. One blend contains 20% basil. Sheilawants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. Let brepresent the amount of basil Sheila should add to the 20% blend.

1. Complete the table representing the problem.

Ounces Amount of Basil

20% Basil Blend

100% Basil

30% Basil Blend

2. Write an equation to represent the problem.

3. How many ounces of basil should Sheila use to make the 30% blend?

4. How many ounces of the 20% blend should she use?

HIKING For Exercises 5–7, use the following information.

At 7:00 A.M., two groups of hikers begin 21 miles apart and head toward each other. The firstgroup, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags, andcooking equipment. The second group, hiking at an average rate of 2 miles per hour, carriesfood and water. Let t represent the hiking time.

5. Copy and complete the table representing the problem.

r t d � rt

First group of hikers

Second group of hikers

6. Write an equation using t that describes the distances traveled.

7. How long will it be until the two groups of hikers meet?

SALES For Exercises 8 and 9, use the following information.

Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. Tomake the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanutsthat cost $3.00 per pound. He mixes 10 pounds at a time.

8. How many pounds of Virginia peanuts does Sergio use?

9. How many pounds of Spanish peanuts does Sergio use?


GRASS SEED For Exercises 1–4, use the following information.

A nursery sells Kentucky Blue Grass seed for $5.75 per pound and Tall Fescue seed for$4.50 per pound. The nursery sells a mixture of the two kinds of seed for $5.25 per pound.Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds ofthe mixture.

1. Complete the table representing the problem.

Number of Pounds Price per Pound Cost

Kentucky Blue Grass

Tall Fescue

Mixture

2. Write an equation to represent the problem.

3. How much Kentucky Blue Grass does the nursery use in 5 pounds of the mixture?

4. How much Tall Fescue does the nursery use in 5 pounds of the mixture?

TRAVEL For Exercises 5–7, use the following information.

Two commuter trains carry passengers between two cities, one traveling east, and the otherwest, on different tracks. Their respective stations are 150 miles apart. Both trains leave atthe same time, one traveling at an average speed of 55 miles per hour and the other at anaverage speed of 65 miles per hour. Let t represent the time until the trains pass each other.

5. Copy and complete the table representing the problem.

r t d � rt

First Train

Second Train

6. Write an equation using t that describes the distances traveled.

7. How long after departing will the trains pass each other?

8. TRAVEL Two trains leave Raleigh at the same time, one traveling north, and the othersouth. The first train travels at 50 miles per hour and the second at 60 miles per hour.In how many hours will the trains be 275 miles apart?

9. JUICE A pineapple drink contains 15% pineapple juice. How much pure pineapple juiceshould be added to 8 quarts of the drink to obtain a mixture containing 50% pineapplejuice?

Practice Weighted Averages

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Pre-Activity How are scores calculated in a figure skating competition?


Why is the sum of Ilia Kulik’s scores divided by 3?

Reading the Lesson

1. Read the definition of weighted average on page 171 of your textbook. What is meant bythe weight of a number in a set of data?

2. Linda’s quiz scores in science are 90, 85, 85, 75, 85, and 90. What is the weight of thescore 85?

3. Suppose Clint drives at 50 miles per hour for 2 hours. Then he drives at 60 miles perhour for 3 hours.

a. Write his speed for each hour of the trip.

Speed

Hour 1 2 3 4 5

b. What is the weight of each of the two speeds?


4. Making a table can be helpful in solving mixture problems. In your own words, explainhow you use a table to solve mixture problems.


Diophantine EquationsThe first great algebraist, Diophantus of Alexandria (about A.D. 300),devoted much of his work to the solving of indeterminate equations.An indeterminate equation has more than one variable and anunlimited number of solutions. An example is x � 2y � 4.

When the coefficients of an indeterminate equation are integers andyou are asked to find solutions that must be integers, the equation iscalled diophantine. Such equations can be quite difficult to solve,often involving trial and error—and some luck!

Solve each diophantine equation by finding at least one pair of positive integers that makes the equation true. Some hints are given to help you.

1. 2x � 5y � 32

a. First solve the equation for x.

b. Why must y be an even number?

c. Find at least one solution.

2. 5x � 2y � 42

a. First solve the equation for x.

b. Rewrite your answer in the form x � 8 � some expression.

c. Why must (2 � 2y) be a multiple of 5?

d. Find at least one solution.

3. 2x � 7y � 29 4. 7x � 5y � 118

5. 8x � 13y � 100 6. 3x � 4y � 22

7. 5x � 14y � 11 8. 7x � 3y � 40

Enrichment

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Chapter 3 Test, Form 1

NAME DATE PERIOD

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Ass

essm

ent

Write the letter for the correct answer in the blank at the right of each question.

1. Solve x � 19 � 5.A. 24 B. 14 C. �24 D. �14 1.

2. Solve y � 18 � �3.A. �21 B. 21 C. �15 D. 15 2.

3. Solve 5n � 35.A. 30 B. 7 C. 40 D. 165 3.

4. Solve �3c

� � 6.

A. 3 B. 9 C. 2 D. 18 4.

5. Solve �35�x � 15.

A. 9 B. 5 C. 25 D. 75 5.

6. Solve 2t � 1 � 3.A. 1 B. �1 C. 2 D. �2 6.

7. Translate the following sentence into an equation.Twice a number m minus three equals the sum of m and five.A. 2(m � 3) � m � 5 B. 2m � 3 � m � 5C. 2m � 3 � 5m D. 2(m � 3) � 5m 7.

8. Translate the following equation into a verbal sentence.x � 5 � 2(7 � x)A. The quotient of x and five is two times seven plus x.B. The number x plus five is two times the sum of seven and x.C. The number x plus five is two times seven plus x.D. The product of x and five is the sum of two times seven and x. 8.

9. A number is added to 9. The result is then multiplied by 4 to give a new result of 120. What is the number?A. 21 B. 39 C. 489 D. 4(n � 9) � 120 9.

10. Which ratio forms a proportion with �174�

?

A. �49� B. �1

52�

C. �25� D. �

36� 10.

33


Chapter 3 Test, Form 1 (continued)

11. Solve the proportion �27� � �4

x2�

.

A. �12� B. 12 C. �

27� D. 6 11.

12. Solve 3t � 6 � t �2.A. �2 B. �4 C. 2 D. 1 12.

13. Solve 4(t � 1) � 6t � 1.A. 2�

12� B. 1 C. 0 D. 1�

12� 13.

14. Solve 5(g � 2) � g � 6(g � 4).A. all numbers B. 0 C. 2 D. no solution 14.

15. Solve ax � 5 � b for a.

A. x(b � 5) B. �b�

x5

� C. �b �

x5

� D. x(b � 5) 15.

16. Find the percent of change. original: 10 new: 12A. 12% B. 25% C. 20% D. 18% 16.

17. A baseball costs $4.00. If the sales tax is 5%, what is the total price?A. $3.80 B. $4.20 C. $4.05 D. $4.50 17.

18. How many liters of pure acid must be added to 3 liters of a 50% acid solution to obtain a 75% acid solution?A. 1 L B. 4.5 L C. 1.5 L D. 3 L 18.

19. Joe and Janna leave home at the same time, traveling in opposite directions. Joe drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will they be 510 miles apart?A. 7 hours B. 6 hours C. 5 hours D. 4 hours 19.

20. TEMPERATURE In Death Valley, California, the highest ground temperature recorded was 94�C on July 15, 1972. In the formula

C � �59�(F � 32), C represents the temperature in degrees Celsius and F

represents the temperature in degrees Fahrenheit. To the nearest degree,what is the highest ground temperature in Death Valley in Fahrenheit?A. 201�F B. 84�F C. 34�F D. 137�F 20.

Bonus A concrete mixture is made with 3 parts water and B:5 parts cement. If 27 parts of water are being used in the current batch of concrete, how many parts of cement are being used?

NAME DATE PERIOD

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Chapter 3 Test, Form 2A

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Ass

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1. Solve m � (�4) � 7.A. 11 B. 3 C. �3 D. �11 1.

2. Solve m � 13 � 8.A. 21 B. �21 C. 5 D. �5 2.

3. Solve 5w � �75.A. 15 B. �80 C. �15 D. 80 3.

4. Solve ��n4� � �12.

A. 3 B. 48 C. �8 D. �16 4.

5. Solve ��38�y � �24.

A. �9 B. 9 C. �64 D. 64 5.

6. Solve 5x � 3 � 23.

A. 4 B. 5�12� C. 25 D. 15 6.

7. Translate the following sentence into an equation.The sum of twice a number x and 13 is two less than three times x.A. 2(x � 13) � 3x � 2 B. 2x � 13 � 2 � 3xC. 2x � 13 � 3x � 2 D. 2x � 13 � 3(x � 2) 7.

8. Translate the following equation into a verbal sentence.3x � y � 5(y � 2x)A. Three times the difference of x and y equals five times the sum of y and

two times x.B. Three times x less than y is five times y plus two times x.C. The sum of three times x and y is five times y plus two times x.D. Three times x minus y is five times the sum of y and two times x. 8.

9. Six is subtracted from a number. The result is divided by four. This result is added to 10 to give 30. What is the number?A. 4 B. 80 C. 86 D. 16 9.

10. Which ratio forms a proportion with �2355�

?

A. �35� B. �

1251�

C. �2344�

D. �150�

10.

33

33


11. Solve the proportion �35c�

� �16�.

A. 2 B. 10 C. 30 D. �131� 11.

12. Solve 2x � 7 � 5x � 16.

A. �3 B. �23� C. �7�

23� D. 3 12.

13. Solve �23�(6x � 30) � x � 5(x � 4) � 2x.

A. 6 B. 0 C. all numbers D. no solution 13.

14. Solve �3(h � 6) � 5(2h � 3).

A. ��133�

B. �133�

C. ��193�

D. �193�

14.

15. Solve 2x � y � y for x.A. 2y � 2 B. y � 2 C. y D. 0 15.

16. Find the percent of change. original: 80 new: 64A. 25% B. 20% C. 16% D. 10% 16.

17. A calculator costs $32.00. If the sales tax is 6%, what is the total price?A. $31.40 B. $30.08 C. $32.60 D. $33.92 17.

18. How many liters of a 40% acid solution must be added to 12 liters of a 20% solution to obtain a 25% solution?A. 4 B. 1 C. 16 D. �

45� 18.

19. Mandy begins bicycling west at 30 miles per hour at 11 A.M. If Liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour,when will she catch Mandy?A. 2:00 P.M. B. 1:00 P.M. C. 1:30 P.M. D. 2:30 P.M. 19.

20. GEOMETRY The formula for the volume of a cone is V � �13��r2h where V

represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?

A. 21 cm B. 69.14 cm C. 7 cm D. 0.78 cm 20.

Bonus A mixture of 10% acid and 90% water is added to 5 liters B:of pure acid. The final mixture is 40% water. How many liters of water are in the final mixture?

NAME DATE PERIOD

Chapter 3 Test, Form 2A (continued)

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1. Solve 4 � n � (�3).A. 1 B. 7 C. �1 D. �7 1.

2. Solve x � 12 � 5.A. �17 B. �7 C. 17 D. 7 2.

3. Solve 6z � �84.A. �90 B. �78 C. �14 D. �504 3.

4. Solve �15 � ��w3�.

A. 5 B. 45 C. �18 D. �12 4.

5. Solve ��47�s � �28.

A. 49 B. �49 C. 16 D. �16 5.

6. Solve 2 � 7y � 44.

A. 6�47� B. 35 C. 49 D. 6 6.

7. Translate the following sentence into an equation.The product of five and a number y is two less than the quotient of four and y.

A. 5 � y � �4y� � 2 B. 5y � �

4y� � 2

C. 5y � 2 � �4y� D. 5 � y � 2 � �

4y� 7.

8. Translate the following equation into a verbal sentence.x(7 � 5y) � �2

x�

A. x times seven minus five times y equals x divided by two.B. The product of x and seven minus five times y equals the quotient of x

and two.C. x times the difference of seven and the product of five and y equals the

quotient of x and two.D. x times the sum of seven and five times y equals x divided by two. 8.

9. A number is divided by four. The result is added to five. This result is multiplied by three to give 27. What is the number?

A. 16 B. 1 C. 21�12� D. 3�

12� 9.

10. What ratio forms a proportion with �386�

?

A. �14� B. �2

67�

C. �370�

D. �27� 10.

33 Chapter 3 Test, Form 2B


11. Solve the proportion �18� � �2

7h�

.

A. 4 B. 28 C. 56 D. 16 11.

12. Solve 9a � 28 � 4a � 3.

A. �30 B. �20 C. 6�15� D. �5 12.

13. Solve 3x � 4(x � 8) � x � �35�(10x � 15).

A. 0 B. all numbers C. no solution D. 41 13.

14. Solve 4(3r � 2) � �3(r � 7).

A. ��1135�

B. �1�145�

C. 1�1145�

D. �1�130�

14.

15. Solve 3b � 6v � 3b, for v.A. 6b � 6 B. b C. b � 6 D. 0 15.

16. Find the percent of change. original: 45 new: 54

A. 33�13�% B. 25% C. 16�

23�% D. 20% 16.

17. Find the discounted price. radio: $45.00 discount: 30%A. $15.00 B. $31.50 C. $36.00 D. $42.00 17.

18. Nature Drinks wants to combine orange juice they sell for $0.09 per ounce with guava juice they sell for $0.14 per ounce to create an orange-guava drink. How many ounces of orange juice should they use to create a 16-ounce drink that would sell for $1.74?A. 10 B. 6 C. 16 D. 0 18.

19. Teri begins walking east at 2 miles per hour at 1 P.M. If Cindy leaves from the same point 30 minutes later walking east at 3 miles per hour, when will she catch Teri?A. 2:30 P.M. B. 1:30 P.M. C. 2:00 P.M. D. 3:00 P.M. 19.

20. GEOMETRY The formula for the volume of a cone is V � �13��r2h, where V

represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 110 cubic centimeters and a base with a radius of 5 centimeters?

A. 21 cm B. 0.47 cm C. 4.2 cm D. 41.49 cm 20.

Bonus In a bag of blue, green, and red marbles, 50% are blue B:and 30% are green. There are 6 red marbles in the bag.If you increase the number of blue marbles by 40%, how many blue marbles will be in the bag?

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NAME DATE PERIOD

Chapter 3 Test, Form 2B (continued)

NAME DATE PERIOD

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For Questions 1–8, solve each equation.

1. 12 � r � 3 1.

2. �15� � x � �

25� 2.

3. �12 � p � 7 3.

4. �7b � �35 4.

5. 31 � ��n6� 5.

6. ��58�w � �9 6.

7. �295�

� �1p25�

7.

8. �3a � 4 � �14 8.

9. Translate the following sentence into an equation. 9.A number x subtracted from 36 is three times the sum of four and x.

10. Translate the following equation into a verbal sentence. 10.3(x � y) � 2y � x

For Questions 11 and 12, write an equation for each problem.Then solve the equation.

11. What number decreased by 3.5 equals 12.7? 11.

12. Twelve is added to the product of a number and 5. 12.The result is �3. Find the number.

13. Solve the following problem by working backward. 13.Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him. She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. She bought a pair of running shoes for $29.45 and had $17.75 left. How much did Julie receive when she cashed her paycheck?

14. Use cross products to determine whether the pair of 14.ratios �

46� and �

1241�

form a proportion. Write yes or no.

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NAME DATE PERIOD

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NAME DATE PERIOD

SCORE Chapter 3 Test, Form 2C


15. Solve the proportion �6x

� � �29�. 15.

16. Solve the proportion �1125�

� �1b8�. 16.


17. �x � 4 � x � 6 17.

18. 5n � 7 � 7(n � 1) � 2n 18.

19. �4(p � 2) � 8 � 2(p � 1) � 7p � 15 19.

20. Solve �ab�x � c � 0 for x. 20.

21. State whether the percent of change is a percent of increase 21.or a percent of decrease. Then find the percent of change.original: 55 new: 44

22. A shirt costs $12.00. If the sales tax is 7%, find the 22.total cost.

23. How many liters of a 90% acid solution must be added to 23.6 liters of a 15% acid solution to obtain a 40% acid solution?

24. A freight train leaves a station traveling 60 miles per hour. 24.Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?

25. GEOMETRY A container company wants to make a 25.cylindrical can with a volume of 1188 cubic inches. The formula V � �r2h represents the volume of a cylinder. In this formula, V represents the volume, r represents the radius of the cylinder’s base, and h represents the height of the cylinder. Solve for h. What height should the company make the can if the radius of the base must be 6 inches?

Bonus A clown is preparing for a party by inflating one balloon B:for every invited guest. Just when she has half of the necessary balloons inflated, 3 of them pop. She inflates 5 more balloons, and two pop. Then 6 balloons are carried away by the wind. She finishes by inflating 16 more balloons, and then learns that only 12 guests will attend the party. How many extra balloons did the clown inflate?

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NAME DATE PERIOD NAME DATE PERIOD

Chapter 3 Test, Form 2C (continued)

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33



1. 7 � t � 11 1.

2. �19� � y � �

59� 2.

3. �5 � v � 12 3.

4. �8x � �56 4.

5. 14 � ��5s

� 5.

6. ��79�y � �6 6.

7. �1207�

� �1a35�

7.

8. 3 � 5b � �32 8.

9. Translate the following sentence into an equation. 9.A number n added to 18 is seven times the difference of n and three.

10. Translate the following equation into a verbal sentence. 10.

�3y� � 5 � x(y � 7)


11. What number decreased by 8.1 equals 4.9? 11.

12. Fifteen is added to the product of a number and 6. 12.The result is 9. Find the number.

13. Solve the following problem by working backward. 13.During an evening out, Dean paid a cab driver $20. He then spent $25 on dinner and half of his remaining money on a painting. He bought an umbrella for $23.75 and had $42.15 left. How much money did Dean have at the beginning of the weekend?

14. Use cross products to determine whether the pair of ratios 14.

�291�

and �1226�


NAME DATE PERIOD

SCORE Chapter 3 Test, Form 2D

33



� �1y5�

. 15.


� �1a5�. 16.


17. 9 � t � t � 3 17.

18. 2(y � 6) � 3y � 12 � y 18.

19. 17 � 3(z � 2) � 11z � �7(z � 2) � 14 19.

20. Solve �rs� � t � 4v for r. 20.

21. State whether the percent of change is a percent of increase 21.or a percent of decrease. Then find the percent of change.original: 60, new: 75

22. Find the discounted price. 22.flashlight: $18.00 discount: 25%

23. Nature’s Best wants to combine nuts they sell for $3.60 a 23.pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound?

24. Paula leaves home driving 40 miles per hour. One hour 24.later, her brother Dan leaves home, driving in the same direction at a speed of 50 miles per hour. How long will it take Dan to catch up to Paula?

25. GEOMETRY A container company wants to make a 25.cylindrical cardboard container with a volume of 4752 cubic inches. The formula V � �r2h represents the volume of a cylinder. In this formula, V represents the volume, rrepresents the radius of the cylinder’s base, and hrepresents the height of the cylinder. Solve for h. What height should the company make the container if the radius of the base must be 9 inches?

Bonus A store has all board games on sale for 25% off the B:regular price. A checker set has a sale price of $12. It is then moved to a clearance table where every item is discounted 40% off its regular price. What is the clearance price of the checker set?

NAME DATE PERIOD

Chapter 3 Test, Form 2D (continued)

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Ass

essm

ent

33



1. n � 39 � 12 1.

2. w � (�8) � �21 2.

3. �6n � 16 3.

4. �13 � ��n4� 4.

5. �34�h � ��

4552�

5.

6. ��a6� � 7 � �14 6.

7. If x � 5 � 12, what is the value of x � 9? 7.

8. Translate the following into an equation. 8.A number x is decreased by 45. The result is then divided by 12. Then 20 is added to this new result to give a final result of five times the difference of 32 and the number x.


9. Three-fifths of what number equals one? 9.

10. The product of 2 more than a number and 10 is 36 more 10.than 8 times the number. What is the number?

11. Translate the following equation into a verbal sentence. 11.5(2x � 3y) � y2 � 2x3

12. Solve the following problem by working backward. 12.Shyam invested money in the stock market. In the first year, his stock increased 20%. He paid his stock broker $300 and then lost $450. He withdrew $500, and then his remaining investment doubled. Shyam’s investment is now worth $7100. How much was Shyam’s original investment?

13. Use cross products to determine whether the pair of ratios 13.

�4428�

and �6732�


14. Solve the proportion �tt��

42� � �

14�. 14.

15. A blueprint for a house states that 2 inches represents 15.8 feet. If the width of a window is 2.5 inches on the blueprint, what is the width of the actual window?

NAME DATE PERIOD

SCORE Chapter 3 Test, Form 3

33



16. 6 � 2y � 7y � 13 16.

17. 3x � 5(x � 6) � 2(10 � x) � 10 17.

18. 5(7 � a) � 3(a � 4) � 4 � 4(a �3) � 7 18.

19. Solve ax � n � r for x. 19.

20. Solve �4xr� t� � s for x. 20.

21. State whether the percent of change is a percent of 21.increase or a percent of decrease. Then find the percent of change.original: 75, new: 84

22. A jacket costs $75.00 retail. A warehouse outlet discounts 22.the price by 20%. If the sales tax is 6%, find the final price.

23. Calvin invested $7500 for one year, part at 12% annual 23.interest and the rest at 10% annual interest. His total interest for the year was $890. How much money did he invest at 12%?

24. Two airplanes leave the Atlanta airport at the same time, 24.traveling in opposite directions. One plane travels 30 miles per hour faster than the other. After 3 hours, the planes are 3150 miles apart. What is the rate of each plane?

25. PHYSICS A ball is thrown straight up at an initial velocity 25.of 53 feet per second. In the first 1.5 seconds, it travels

42 feet. The formula s � ��u �2

v�� t represents the vertical

distance s that an object travels in t seconds, where urepresents the initial velocity of the object and v represents the velocity of the object at the end of t seconds. Find the velocity of the ball at the end of 1.5 seconds.

Bonus Paloma Rey drove to work on Wednesday at 40 miles B:per hour and arrived one minute late. She left home at the same time on Thursday, drove 45 miles per hour,and arrived one minute early. How far does Ms. Rey drive to work?

NAME DATE PERIOD

Chapter 3 Test, Form 3 (continued)

NAME DATE PERIOD NAME DATE PERIOD

Chapter 3 Open-Ended Assessment


Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.

1. Phrase 1: x times y plus zPhrase 2: x times the sum of y and za. Discuss what is different between the two phrases.b. Find values for x, y and z that make the two phrases equal.

2. a. Solve �rym� s� � t � x for y, and explain each step in your

solution.b. Would there be any limitations for the value of each variable?

If so, explain the limitation.

3. You buy a stereo at a local store. The stereo has been discountedby 10%. The store then charges 10% tax.a. Compare the final price with the original price.b. Would the final price be different if the tax was added first

and then the discount was applied to this new amount?

4. Tony and Ivia started walking south from the same location atthe same time. Ivia walked 8 miles and walked 1 mile per hourfaster than Tony who walked 6 miles. They each walked for thesame amount of time.a. Describe how a proportion could be used to find the rate that

each person walked.b. The next day they both walked 6 miles, and Ivia again walked

1 mile per hour faster than Tony, who walked 3 miles per hour.Determine whether a proportion could be used to find howlong each person walked.

5. a. Write four equivalent equations to x � 8 using one of the fouroperations of addition, subtraction, multiplication and divisionfor each equivalent equation. Use each operation only once.

b. Write an equivalent equation to x � 8 that has the variable xon both sides.

c. Determine if �n6� � �

1158�

and 2(n � 1) � 3(n � 1) are equivalent

equations. Determine if either equation is equivalent to any ofthe equations created for parts a and b.

NAME DATE PERIOD

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Ass

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Chapter 3 Vocabulary Test/Review

Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.

1. The Addition Property of Equality states that if the same 1.number is subtracted from each side of an equation, the resulting equation is true.

2. If the same number is added to each side of a true equation, 2.then the result is a true equation.

3. The Multiplication Property of Equality states that if each 3.side of a true equation is multiplied by the same number,the resulting equation is true.

4. Multi-step equations are equations with less than one 4.operation.

5. An equation that is false for every value of the variable is 5.called an identity.

6. A ratio is a comparison of two numbers by multiplication. 6.

7. The ratio of two measurements having different units of 7.measure is called a rate.

8. A percent of increase or decrease is called a 8.percent of change.

9. If the new number is less than the original number, the 9.percent of change is a percent of increase.

10. If the new number is greater than the original number, the 10.percent of change is a percent of decrease.

In your own words—Define each term.

11. proportion

12. formula

Addition Property of Equalityconsecutive integersdefining a variabledimensional analysisDivision Property of Equalityequivalent equationextremesformulafour-step problem-solving planidentity

meansmixture problemMultiplication Property of Equality

multi-step equationsnumber theorypercent of changepercent of decreasepercent of increaseproportion

rateratioscalesolve an equationSubtraction Property of Equality

uniform motion problemweighted averagework backward

NAME DATE PERIOD

SCORE 33

NAME DATE PERIOD

SCORE

Chapter 3 Quiz (Lessons 3–1 through 3–3)33



1. Two times a number n is three times the sum of n and nine. 1.

2. The difference of the square of y and twelve is the same as 2.the product of five and x.


3. 2b � 10 � 4 4. y � 3x2 � 5x

Solve each equation.

5. d � 8 � 6 6. �28 � p � 21

7. �3 � (�g) � �12 8. �7x � 63

9. ��5t� � �8 10. �

45�d � �32

NAME DATE PERIOD

SCORE

Chapter 3 Quiz (Lessons 3–4 and 3–5)

Solve each equation.

1. 3x � 8 � 29 2. �a6� � 5 � 9

3. 5r � 14 � �42 4. 7n � 6 � 4n � 9

5. 3b � 13 � 4b � 7b � 1 6. 5 � 3(w � 4) � w � 7

7. 2x � 5(x � 3) � 2(x � 10)

8. Standardized Test Practice Solve �6(2r � 8) � �10(r � 3).A. �11 B. �156 C. �39 D. 9


9. A number is multiplied by 4, and then 5 is subtracted from the product. The result is 3. What is the number?

10. Three is subtracted from a number, and then the difference is divided by 11. The result is 12. What is the number?

NAME DATE PERIOD

SCORE 33

Ass

essm

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3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Use cross products to determine whether each pair of ratios forms a proportion. Write yes or no.

1. �57�, �

2208�

2. �1113�

, �2225�

3. �46..23�

, �00..35�

Solve each proportion.

4. �34� � �2

n0�

5. �64� � �1

x8�

6. �3b3� � �

1455�

For Questions 7 and 8, state whether the percent of change is a percent of increase or a percent of decrease.Then find the percent of change.


9. The cost of a compact disc is $18. If the sales tax is 6%, 9.find the total price.

10. Find the discounted price. camera: $108 10.discount: 30%

Chapter 3 Quiz (Lessons 3–8 and 3–9)

For Questions 1 and 2, solve each equation or formula for the variable specified.

1. nx � m � p, for x 1.

2. �x �

ab

� � c, for b 2.

3. A chemist needs a 30% iron alloy. How many grams of a 3.70% iron alloy must be mixed with 16 grams of a 20% iron alloy to obtain the required 30% alloy?

4. On Mary’s walk she covered the 3-mile distance to the park 4.in one hour. However, the return trip took her one and a half hours. What was her average speed for the round trip?

5. The formula p � 2� � 2w represents the perimeter of a 5.rectangle. In this formula, � is the length of the rectangle and w is the width. Solve the formula for �. Find the length when the width is 4 meters and the perimeter is 36 meters.

NAME DATE PERIOD

SCORE

Chapter 3 Quiz (Lessons 3–6 and 3–7)33

NAME DATE PERIOD

SCORE

33

1.

2.

3.

4.

5.

6.

7.

8.

Chapter 3 Mid-Chapter Test (Lessons 3–1 through 3–5)



1. Translate the following sentence into an equation.The product of five and the sum of a number x and three is twelve.A. 5 � 3x � 12 B. 5(x � 3) �12C. 5x � 3 �12 D. 5x � 3 �x 1.

2. Solve y � (�16) � �12.A. 192 B. �28 C. �

34� D. 4 2.

3. Solve ��a6� � 5 � 2.

A. 18 B. �6 C. �12� D. �9 3.

4. Solve �35�y � �9.

A. �5�25� B. �5 C. �15 D. ��

59� 4.

5. Solve �6d � �42.A. �48 B. 7 C. �36 D. 252 5.

6. Solve �18 � v � (�4).A. 22 B. �14 C. �22 D. 14 6.


7. 5(12 � 3p) � 15p � 60 7.

8. 3(y � 2) � 6(y � 1) � 3y 8.

9. 3a � 21 � 7 � 4a 9.

10. Solve the following problem by working backward. 10.Liza earned some money delivering newspapers. She bought a battery for $1.95, and gave her mother $30. She bought a ring for $7.20, and then spent half of the remaining money on a radio. If Liza has $38.50 left, how much money did she earn delivering newspapers?

For Questions 11 and 12, translate each equation into a verbal sentence.

11. 4n � m(5 � n) 11.

12. 3(y � 5) � 7y 12.

Part II

Part I

NAME DATE PERIOD

SCORE 33

Ass

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Chapter 3 Cumulative Review (Chapters 1–3)

1. Evaluate 3y � x2z if x � 2, y � 14, and z � 5. (Lesson 1–2) 1.

2. Simplify 2(u � 3v) � 3(u � v). (Lesson 1–6) 2.

3. Miguel was riding his bike to school. He got halfway there 3.and realized he had forgotten his backpack. He turned around, went home, retrieved his backpack, and continued his ride to school. Sketch a reasonable graph to show his distance from school from the time he started to the time he arrived at school. Assume his rate is always the same.(Lesson 1–8)

Find each of the following. (Lessons 2–2 through 2–4, 2–7)

4. 13.7 � (�3.2) 5. 12(�32) 6.

6. 52 � (�4) 7. ��1.69� 7.

8. The values of the 14 highest recorded temperatures in the 8.United States are listed below.128 120 134 118 118 121 125122 121 120 119 120 120 118 Source: World Almanac

Make a line plot of the data. (Lesson 2–5)

9. A baseball player has a batting average of 0.250. What are 9.the odds that the next time the player bats he gets a hit?(Lesson 2–6)

10. Translate the following sentence into an algebraic equation. 10.Nine times a number y subtracted from 85 is seven times the sum of four and y. (Lesson 3–1)

11. Solve the following problem by working backward. Three is 11.added to a number. The result is divided by two, and then the new result is added to eighteen. The final result is 35.What is the number? (Lesson 3–4)

For Questions 12–14, solve each equation.(Lessons 3–2 through 3–5)

12. �27 � �6 � 3p 13. 7a � 2 �3a � 10

14. 2(x �3) � 6x � 3(9 � x) 14.

15. Solve q � �mn� � p for m. (Lesson 3–8) 15.

16. How many liters of water must be added to 7 liters of a 16.20% acid solution to obtain a 10% acid solution?(Lesson 3–9)

115 120 125 130 135

NAME DATE PERIOD

33

NAME DATE PERIOD

SCORE

4.

5.

12.

13.

Standardized Test Practice (Chapters 1–3)


1. Write an algebraic expression for the following verbal expression.The sum of n and 5. (Lesson 1–1)

A. 5n B. �n5� C. n � 5 D. n � 5 1.

2. State the hypothesis of the following statement.If I complete my algebra homework daily, then I will learn the concepts. (Lesson 1–7)

E. I will learn the concepts.F. I don’t do my algebra homework.G. I won’t learn the concepts.H. I complete my algebra homework daily. 2.

3. Simplify the expression 7(x � y) � 2(y � x) � 4x. (Lesson 1–5)

A. 13x � 9y B. 9x � 5y C. 9x � 9y D. 13x � 5y 3.

4. Evaluate a(b � c2) if a � �23�, b � �

34�, and c � �

12�. (Lesson 2–3)

E. �16� F. �

13� G. �

14� H. �

23� 4.

5. The heights in feet of the 10 largest National Champion trees are listed below. Source: World Almanac

275 321 159 191 281 83 108 232 219 102Which measure of central tendency best represents the data? (Lesson 2–5)

A. the mode B. the mean or the medianC. the mean or the mode D. the median or the mode 5.

6. A letter is chosen at random from the name Antarctica. What is the probability that the chosen letter is a vowel? (Lesson 2–6)

E. �25� F. �1

30�

G. �12� H. �

35� 6.

7. Solve ��34�y � �2

80�

. (Lesson 3–3)

A. �25� B. � �1

30�

C. �185�

D. ��185�

7.

8. Which equation has a solution of �2? (Lesson 3–4)

E. 4n � 3 � 11 F. 4 � 3n � 2G. 5(1 � n) � �5 H. 3(n � 1) � 2 8.

9. A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot? (Lesson 3–7)

A. 230 B. 225 C. 135 D. 205 9. DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

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Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

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Standardized Test Practice (continued)

10. Solve 2�13� � �

56� � t. (Lesson 1–3)

11. Find �13� � ( � �

14�). (Lesson 2–2)

12. Solve 7 � 3x � 4 � 9x. (Lesson 3–5)

13. Sasha drove from her house to the grocerystore in 20 minutes. Her return trip took 15 minutes. If the store is 7 miles from herhouse, what was Sasha’s average speed for the round trip, in miles per hour? (Lesson 3–9)

Column A Column B

14. 14.

(Lesson 1–4)

15. Let u � 4, v � �3, and t � 2. 15.

(Lesson 2–4)

16. Let �7x

� � �1228�

. 16.

(Lesson 3–6)

DCBA

DCBA

DCBA

Part 3: Quantitative Comparison

Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.

NAME DATE PERIOD

33

10. 11.

12. 13.

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

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Part 2: Grid In

Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.

A

D

C

B

(4 � 1 � 4) � �15

�(10 � 5) (2 � 0)��12

�� 5(7 � 3 � 2)

uv � t u � vt

�9x

� �1x

�

Unit 1 Test(Chapters 1–3)


1. Write an algebraic expression for 1.the difference of 5 and n cubed.

2. Evaluate 2x � 5y2 � 3z if x � 6, y � 4, and z � 7. 2.

3. Find the solution set for 3b � 4 � 8 if the replacement set 3.is {1, 2, 3, 4, 5}.

4. Name the property used in the equation 1 � 6n. Then find 4.the value of n.

For Questions 5–7, simplify each expression.

5. 2t2 � 5t2 � 3t 5.

6. 7(r � 2t) � 5t 6.

7. 5(4a � b) � 3a � b 7.

8. Identify the hypothesis and conclusion of the statement. 8.Then write the statement in if-then form.All triangles are polygons.

9. Draw a reasonable graph showing the relationship between 9.the temperature of a pizza as it is removed from an oven and placed on a counter at room temperature, and time.

10. A recent survey asked consumers to identify their favorite ice cream topping. The results are displayed in the circle graph. If 250 people were 10.surveyed, how many chose strawberries as their favorite topping?

11. Graph {4, 5, 6, 7, 8, …}. 11.

Find each sum, product, or quotient.

12. 31 � (�78) 12.

13. ��89��

34�� 13.

14. 37.6 � (�8) 14.

15. A card is selected at random from a standard deck of 15.52 cards. What is the probability of selecting a diamond?

16. Find the odds of rolling a number less than 6 on a die. 16.

�2�3 �1 0 1 2 4 5 6 7 83

TimeTe

mp

erat

ure

(F°

)

Ass

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NAME DATE PERIOD

SCORE

Other18%

Caramel9%

Strawberries16%Chocolate

Syrup28%

Hot Fudge29%

NAME DATE PERIOD

SCORE


Unit 1 Test (continued)

For Questions 17 and 18, use the list that shows the number of hours Mrs. Wentworth’s piano students spent practicing last week.

9 2 2 4 14 2 7 1 5 0 3 1 3 9 11 2

17. Make a line plot of the data. 17.

18. Which measure of central tendency best describes the data? 18.Explain.

19. Name the set or sets of numbers to which �48� belongs. 19.

20. Write �3.6�5�, �13�, �7251�

, ��158� in order from least to greatest. 20.


21. m � 5 � �23 21.

22. �4 � 8 � k 22.

23. �a2

� � 9 � 30 23.

24. ��27

�x � �16 24.

25. 5(c � 3) � 15 � 2(2c � 1) 25.

26. 10(a � 1) � 14a � 9 � (4a � 1) 26.

27. �170� � �

x �

31

� 27.

28. A magazine is on sale for 15% off the original price. If the 28.original price of the magazine is $4.60, what is the discounted price?

29. Solve �t �

rv

� � s, for v. 29.

30. How many pounds of peanuts costing $3.00 a pound should 30.be mixed with 4 pounds of cashews costing $4.50 a pound to obtain a mixture costing $3.50 a pound?

NAME DATE PERIOD

Standardized Test PracticeStudent Record Sheet (Use with pages 186–187 of the Student Edition.)

© Glencoe/McGraw-Hill A1 Glencoe Algebra 1

Select the best answer from the choices given and fill in the corresponding oval.

1 4 7

2 5 8

3 6

Solve the problem and write your answer in the blank.

For Questions 10, 12, and 14, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.

9 10 12 14

10 (grid in)

11

12 (grid in)

13

14 (grid in)

15

Select the best answer from the choices given and fill in the corresponding oval.

16

17

18

Record your answers for Questions 19–20 on the back of this paper.

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.

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DCBADCBA

DCBADCBADCBA

DCBADCBADCBA

NAME DATE PERIOD

33

An

swer

s

Part 3 Quantitative ComparisonPart 3 Quantitative Comparison

Part 2 Short Response/Grid InPart 2 Short Response/Grid In

Part 4 Open-EndedPart 4 Open-Ended

Part 1 Multiple ChoicePart 1 Multiple Choice


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Th

e an

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Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

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Tra

nsl

ate

each

sen

ten

ce i

nto

an

eq

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ion

or

form

ula

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hre

e ti

mes

a n

um

ber

tm

inu

s tw

elve

equ

als

fort

y.3t

�12

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hal

f of

th

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of

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is 5

4.(a

�b

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54

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hre

e ti

mes

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e su

m o

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and

4 is

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rmat

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Lou

wan

ts t

o lo

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t to

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diti

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a p

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wei

ghs

160

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nds

now

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wan

ts t

o w

eigh

150

pou

nds

.

5.If

pre

pres

ents

th

e n

um

ber

of p

oun

ds h

e w

ants

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te a

n e

quat

ion

to

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tth

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itu

atio

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160

�p

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0

6.H

ow m

any

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s h

e n

eed

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ose

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each

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ual

s tw

elve

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b.

a2

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a2�

b2�

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Th

e su

m o

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uar

es o

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b is

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1.4a

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inu

s 5

is e

qu

al t

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10 a

nd

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eq

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tim

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.

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y�

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x2�

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6 ti

mes

th

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rod

uct

of

xan

d y

is

Th

e su

m o

f th

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uar

es o

f x

and

eq

ual

to

24.

y is

eq

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to

8.

5.p

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6.b

�(h

�1)

Th

e su

m o

f p

and

3 is

eq

ual

to

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is

of

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dif

fere

nce

of

han

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.2

tim

es p

.

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0 �

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3(g

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100

min

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mes

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m o

f g

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his

12.

to 8

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)

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mes

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al t

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fere

nce

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p is

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b

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o

f th

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uct

of

Ais

eq

ual

to

o

f th

e p

rod

uct

of

Ban

d h

.h

and

b.

1 � 21 � 3

1 � 21 � 3

5 � 9

5 � 91 � 31 � 3

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

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)

Wri

tin

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qu

atio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

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3-1

3-1

Exam

ple

Exam

ple

Exer

cises

Exer

cises

Answers (Lesson 3-1)


An

swer

s

Skil

ls P

ract

ice

Wri

tin

g E

qu

atio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-1

3-1

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Lesson 3-1

Tra

nsl

ate

each

sen

ten

ce i

nto

an

eq

uat

ion

.

1.T

wo

adde

d to

th

ree

tim

es a

nu

mbe

r m

is t

he

sam

e as

18.

3m�

2 �

18

2.T

wic

e a

incr

ease

d by

th

e cu

be o

f a

equ

als

b.2a

�a

3�

b

3.S

even

les

s th

an t

he

sum

of

pan

d q

is a

s m

uch

as

6.(p

�q

) �

7 �

6

4.T

he

sum

of

xan

d it

s sq

uar

e is

equ

al t

o y

tim

es z

.x

�x

2�

yz

5.F

our

tim

es t

he

sum

of

fan

d g

is i

den

tica

l to

six

tim

es g

.4

(f�

g)

�6g

Tra

nsl

ate

each

sen

ten

ce i

nto

a f

orm

ula

.

6.T

he

peri

met

er P

of a

squ

are

equ

als

fou

r ti

mes

th

e le

ngt

h o

f a

side

s.

P�

4s

7.T

he

area

Aof

a s

quar

e is

th

e le

ngt

h o

f a

side

ssq

uar

ed.

A�

s2

8.T

he

peri

met

er P

of a

tri

angl

e is

equ

al t

o th

e su

m o

f th

e le

ngt

hs

of s

ides

a,b

,an

d c.

P�

a�

b�

c9.

Th

e ar

ea A

of a

cir

cle

is p

i ti

mes

th

e ra

diu

s r

squ

ared

.A

��

r2

10.T

he

volu

me

Vof

a r

ecta

ngu

lar

pris

m e

qual

s th

e pr

odu

ct o

f th

e le

ngt

h �

,th

e w

idth

w,

and

the

hei

ght

h.

V�

�wh

Tra

nsl

ate

each

eq

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ion

in

to a

ver

bal

sen

ten

ce.

11.g

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p�

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plu

s 10

is t

he

sam

e as

Twic

e p

plu

s 4

tim

es q

is 2

0.3

tim

es g

.

13.4

(a�

b) �

9a14

.8 �

6x�

4 �

2x4

tim

es t

he

sum

of

aan

d b

8 m

inu

s 6

tim

es x

is 4

plu

s

is 9

tim

es a

.2

tim

es x

.

15.

(f�

y) �

f�

516

.s2

�n

2�

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Hal

f o

f th

e su

m o

f f

and

yis

s

squ

ared

min

us

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uar

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f

min

us

5.tw

ice

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te a

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ble

m b

ased

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ven

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atio

n.

17.c

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nn

erc

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er p

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cost

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% t

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�(c

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he

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of

two

po

un

ds

Sam

ple

an

swer

:Th

e co

st o

fo

f p

lain

co

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bea

ns

plu

s o

ne

po

un

d o

fd

inn

er p

lus

a 15

% t

ip w

as

flav

ore

d b

ean

s is

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.Ho

w m

uch

do

es

$23.

Ho

w m

uch

was

th

e 1

po

un

d o

f p

lain

bea

ns

cost

?d

inn

er?

1 � 2

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Tra

nsl

ate

each

sen

ten

ce i

nto

an

eq

uat

ion

.

1.F

ifty

-th

ree

plu

s fo

ur

tim

es c

is a

s m

uch

as

21.

53 �

4c�

21

2.T

he

sum

of

five

tim

es h

and

twic

e g

is e

qual

to

23.

5h�

2g�

23

3.O

ne

fou

rth

th

e su

m o

f r

and

ten

is

iden

tica

l to

rm

inu

s 4.

(r�

10)

�r

�4

4.T

hre

e pl

us

the

sum

of

the

squ

ares

of

wan

d x

is 3

2.3

�(w

2�

x2 )

�32

Tra

nsl

ate

each

sen

ten

ce i

nto

a f

orm

ula

.

5.D

egre

es K

elvi

n K

equ

als

273

plu

s de

gree

s C

elsi

us

C.

K�

273

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6.T

he

tota

l co

st C

of g

as i

s th

e pr

ice

ppe

r ga

llon

tim

es t

he

nu

mbe

r of

gal

lon

s g.

C�

pg

7.T

he

sum

S o

f th

e m

easu

res

of t

he

angl

es o

f a

poly

gon

is

equ

al t

o 18

0 ti

mes

th

e di

ffer

ence

of t

he

nu

mbe

r of

sid

es n

and

2.S

�18

0(n

�2)

Tra

nsl

ate

each

eq

uat

ion

in

to a

ver

bal

sen

ten

ce.

8.q

�(4

�p)

�q

qm

inu

s th

e su

m

9.t

�2

�t

of

4 an

d p

eq

ual

s ti

mes

q.

Two

mo

re t

han

o

f t

equ

als

t.

10.9

(y2

�x)

�18

9 ti

mes

th

e su

m

11.2

(m�

n)

�v

�7

Twic

e th

e q

uan

tity

o

f y

squ

ared

an

d x

is 1

8.m

min

us

nis

vp

lus

7.

Wri

te a

pro

ble

m b

ased

on

th

e gi

ven

in

form

atio

n.

12.a

�co

st o

f on

e ad

ult

’s t

icke

t to

zoo

13.c

�re

gula

r co

st o

f on

e ai

rlin

e ti

cket

a�

4 �

cost

of

one

chil

dren

’s t

icke

t to

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0.20

c�

amou

nt o

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% p

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nal

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ount

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amp

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er:T

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cost

of

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amp

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nsw

er:T

he

cost

of

thre

e ad

ult

’s t

icke

ts a

nd

4 c

hild

ren

’s

airl

ine

tick

ets

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are

dis

cou

nte

d

tick

ets

to t

he

zoo

is $

38.H

ow

20

% is

$33

0.W

hat

is t

he

reg

ula

r m

uch

is a

n a

du

lt’s

tic

ket?

cost

of

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cket

?

14.G

EOG

RA

PHY

Abo

ut

15%

of

all

fede

rall

y-ow

ned

lan

d in

th

e 48

con

tigu

ous

stat

es o

f th

eU

nit

ed S

tate

s is

in

Nev

ada.

If F

repr

esen

ts t

he

area

of

fede

rall

y-ow

ned

lan

d in

th

ese

stat

es,a

nd

Nre

pres

ents

th

e po

rtio

n i

n N

evad

a,w

rite

an

equ

atio

n f

or t

his

sit

uat

ion

.0.

15F

�N

FITN

ESS

For

Exe

rcis

es 1

5–17

,use

th

e fo

llow

ing

info

rmat

ion

.D

ean

na

and

Pie

tra

each

go

for

wal

ks a

rou

nd

a la

ke a

few

tim

es p

er w

eek.

Las

t w

eek,

Dea

nn

a w

alke

d 7

mil

es m

ore

than

Pie

tra.

15.I

f p

repr

esen

ts t

he

nu

mbe

r of

mil

es P

ietr

a w

alke

d,w

rite

an

equ

atio

n t

hat

rep

rese

nts

th

eto

tal

nu

mbe

r of

mil

es T

the

two

girl

s w

alke

d.T

�p

�(p

�7)

16.I

f P

ietr

a w

alke

d 9

mil

es d

uri

ng

the

wee

k,h

ow m

any

mil

es d

id D

ean

na

wal

k?16

mi

17.I

f P

ietr

a w

alke

d 11

mil

es d

uri

ng

the

wee

k,h

ow m

any

mil

es d

id t

he

two

girl

s w

alk

toge

ther

?29

mi

3 � 51 � 3

3 � 51 � 3

1 � 4

Pra

ctic

e (

Ave

rag

e)

Wri

tin

g E

qu

atio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-1

3-1



Readin

g t

o L

earn

Math

em

ati

csW

riti

ng

Eq

uat

ion

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-1

3-1

©G

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Lesson 3-1

Pre-

Act

ivit

yH

ow a

re e

qu

atio

ns

use

d t

o d

escr

ibe

hei

ghts

?

Rea

d th

e in

trod

uct

ion

to

Les

son

3-1

at

the

top

of p

age

120

in y

our

text

book

.

Doe

s th

e eq

uat

ion

305

�s

�15

4 al

so r

epre

sen

t th

e si

tuat

ion

?E

xpla

in.

Yes;

the

tota

l hei

gh

t m

inu

s th

e h

eig

ht

of

the

stat

ue

itse

lf g

ives

the

hei

gh

t o

f th

e p

edes

tal.

Rea

din

g t

he

Less

on

1.T

ran

slat

e ea

ch s

ente

nce

in

to a

n e

quat

ion

.

a.Tw

otim

esth

e su

m o

f x

and

thre

em

inus

four

equa

lsfo

urtim

esx.

2�

(x�

3)�

4�

4�

x

b.

The

diff

eren

ce o

f k

and

3is

two

times

kdi

vide

d by

five.

k�

3�

2�

k�

5

2.A

1 o

z se

rvin

g of

ch

ips

has

140

cal

orie

s.T

her

e ar

e ab

out

14 s

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ag.

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re t

her

e in

a b

ag o

f ch

ips?

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te w

hat

you

r so

luti

on w

ould

be

as y

ouu

se e

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ste

p in

th

e F

our-

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p P

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ng

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n.

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lore

Wh

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?

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as 1

40 c

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d t

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serv

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ips

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bag

.W

hat

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t to

kn

ow?

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w m

any

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ries

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nW

rite

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her

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xam

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9.10

.

En

rich

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NA

ME

____

____

____

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____

____

____

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____

____

____

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AT

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ER

IOD

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3-1

3-1



An

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s

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3-2

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Lesson 3-2

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3-2

3-2

Exam

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Skil

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3-2

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HIS

TORY

For

Exe

rcis

es 2

8 an

d 2

9,u

se t

he

foll

owin

g in

form

atio

n.

Gal

ileo

Gal

ilei

was

bor

n i

n 1

564.

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y ye

ars

late

r,in

164

2,S

ir I

saac

New

ton

was

bor

n.

28.W

rite

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add

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n e

quat

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t th

e si

tuat

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.15

64 �

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1642

29.H

ow m

any

year

s af

ter

Gal

ileo

was

bor

n w

as I

saac

New

ton

bor

n?

78

HU

RR

ICA

NES

For

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rcis

es 3

0 an

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1,u

se t

he

foll

owin

g in

form

atio

n.

Th

e da

y af

ter

a h

urr

ican

e,th

e ba

rom

etri

c pr

essu

re i

n a

coa

stal

tow

n h

as r

isen

to

29.7

in

ches

of

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cury

,wh

ich

is

2.9

inch

es o

f m

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ry h

igh

er t

han

th

e pr

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re w

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eey

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th

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ican

e pa

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____

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____

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AT

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ER

IOD

____

_

3-2

3-2



An

swer

s

Readin

g t

o L

earn

Math

em

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csS

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ing

Eq

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s by

Usi

ng

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dit

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d S

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n

NA

ME

____

____

____

____

____

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____

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AT

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____

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ER

IOD

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3-2

3-2

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use

d t

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are

dat

a?

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d th

e in

trod

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to

Les

son

3-2

at

the

top

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age

128

in y

our

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In t

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�66

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the

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ical

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d t

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per

cen

t o

f g

row

th f

or

trav

el a

gen

ts,

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the

nu

mbe

r 66

rep

rese

nts

the

rate

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gro

wth

fo

r tr

avel

ag

ents

.

Rea

din

g t

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Less

on

1.T

o so

lve

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17 �

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sin

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Pro

pert

y of

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alit

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ould

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btra

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o so

lve

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ng

the

Add

itio

n P

rope

rty

of E

qual

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ld a

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ach

sid

e.

3.W

rite

an

equ

atio

n t

hat

you

cou

ld s

olve

by

subt

ract

ing

32 f

rom

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h s

ide.

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ple

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stu

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Su

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atio

n.E

xpla

in w

hy

itw

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als

o be

pos

sibl

e to

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th

e A

ddit

ion

Pro

pert

y of

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alit

y to

sol

ve t

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equ

atio

n.

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btr

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ng

on

e n

um

ber

fro

m a

no

ther

giv

es t

he

sam

e re

sult

as

add

ing

the

op

po

site

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the

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mb

er t

hat

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su

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ou

Rem

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xpla

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her

to

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e A

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Pro

pert

y or

th

e S

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alit

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ve a

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.S

amp

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he

giv

en e

qu

atio

n h

as a

nu

mb

er a

dd

ed t

o t

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vari

able

,th

en u

se t

he

Su

btr

acti

on

Pro

per

ty o

f E

qu

alit

y.If

th

e eq

uat

ion

has

a n

um

ber

su

btr

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rom

th

e va

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use

th

e A

dd

itio

nP

rop

erty

of

Eq

ual

ity.

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Co

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Sol

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tart

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wit

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,th

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om

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rt o

ver

wit

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h

pers

on w

ho

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s ou

t of

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rcle

.W

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last

per

son

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um

ber

15

2.F

orty

peo

ple

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d in

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nt

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ry t

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d pe

rson

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ich

tw

o pe

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th

e la

st o

nes

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th a

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h p

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3.O

nly

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f of

th

e 30

stu

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ts i

n

Sh

aron

’s c

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aron

arr

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s th

e bo

ys

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girl

s as

sh

own

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ey c

oun

t of

f fr

om 1

to

9 an

d ev

ery

nin

thpe

rson

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ps o

ut

un

til

only

15

peo

ple

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.Wh

o ge

ts t

o go

on

th

e fi

eld

trip

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e g

irls

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rou

p o

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eop

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tan

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n a

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cle

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d

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n.E

very

sec

ond

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son

dro

ps

out.

Per

son

nu

mb

er 1

is

the

last

per

son

lef

t.

4.D

raw

a d

iagr

am t

o sh

ow w

hy

the

nu

mbe

r of

peo

ple

in t

he

circ

le m

ust

be

even

.Th

en,e

xpla

in y

our

answ

er.

If t

he

nu

mb

er

is o

dd

,per

son

1 w

ou

ld d

rop

ou

t af

ter

the

firs

t ro

un

d.

5.W

hen

th

e co

un

t re

turn

s to

per

son

nu

mbe

r 1

for

the

firs

t ti

me,

how

man

y pe

ople

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e dr

oppe

d ou

t?h

alf

of

the

ori

gin

al n

um

ber

6.F

ind

the

nu

mbe

r of

peo

ple

in t

he

circ

le i

f th

e n

um

ber

is

betw

een

10

and

20.D

o th

e sa

me

if t

he

nu

mbe

r is

bet

wee

n

30 a

nd

40.W

hat

can

you

con

clu

de a

bou

t th

e or

igin

al

nu

mbe

r of

peo

ple?

16;

32;T

he

nu

mb

er m

ust

be

a p

ow

er o

f 2.

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3-2

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ult

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____

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sam

en

um

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the

resu

ltin

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uat

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is

equ

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give

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ne.

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can

use

th

e pr

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ty t

oso

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atio

ns

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lvin

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ampl

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ampl

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ampl

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3.F

ind

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s 6.

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To

solv

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uat

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s w

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mu

ltip

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an

d di

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ou c

an a

lso

use

th

e D

ivis

ion

Pro

pert

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alit

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eac

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ide

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n e

quat

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num

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n �

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ME

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UB

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Tw

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RO

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For

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s th

en

um

ber?

84

3.T

wo

is s

ubt

ract

ed f

rom

a n

um

ber,

and

then

th

e di

ffer

ence

is

mu

ltip

lied

by

5.T

he

resu

ltis

30.

Fin

d th

e n

um

ber.

8

4.B

IRD

WA

TCH

ING

Wh

ile

Mic

hel

le s

at o

bser

vin

g bi

rds

at a

bir

d fe

eder

,on

e fo

urt

h o

f th

ebi

rds

flew

aw

ay w

hen

th

ey w

ere

star

tled

by

a n

oise

.Tw

o bi

rds

left

th

e fe

eder

to

go t

oan

oth

er s

tati

oned

a f

ew f

eet

away

.Th

ree

mor

e bi

rds

flew

in

to t

he

bran

ches

of

a n

earb

ytr

ee.F

our

bird

s re

mai

ned

at

the

feed

er.H

ow m

any

bird

s w

ere

at t

he

feed

er i

nit

iall

y?12

Sol

ve e

ach

eq

uat

ion

.Th

en c

hec

k y

our

solu

tion

.

5.�

12n

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�77

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6.17

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7.15

t�

4 �

493

8.�

6 �

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209.

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10.

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��

212

11.

y�

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32 �

f�

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13.8

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g�

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219

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3

Wri

te a

n e

qu

atio

n a

nd

sol

ve e

ach

pro

ble

m.

20.S

even

les

s th

an f

our

tim

es a

nu

mbe

r eq

ual

s 13

.Wh

at i

s th

e n

um

ber?

4n�

7 �

13;

5

21.F

ind

two

con

secu

tive

odd

in

tege

rs w

hos

e su

m i

s 11

6.n

�(n

�2)

�11

6;57

,59

22.F

ind

two

con

secu

tive

eve

n i

nte

gers

wh

ose

sum

is

126.

n�

(n�

2) �

126;

62,6

4

23.F

ind

thre

e co

nse

cuti

ve o

dd i

nte

gers

wh

ose

sum

is

117.

n�

(n�

2) �

(n�

4) �

117;

37,3

9,41

24.C

OIN

CO

LLEC

TIN

GJu

ng

has

a t

otal

of

92 c

oin

s in

his

coi

n c

olle

ctio

n.T

his

is

8 m

ore

than

th

ree

tim

es t

he

nu

mbe

r of

qu

arte

rs i

n t

he

coll

ecti

on.H

ow m

any

quar

ters

doe

s Ju

ng

hav

e in

his

col

lect

ion

?28

x � 7

3k�

7�

515

�a

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r�

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12

3 � 83 � 5

7 � 81 � 8

1 � 2

b � 3d

� �4

u � 5

Pra

ctic

e (

Ave

rag

e)

So

lvin

g M

ult

i-S

tep

Eq

uat

ion

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

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ER

IOD

____

_

3-4

3-4



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csS

olv

ing

Mu

lti-

Ste

p E

qu

atio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

3-4

3-4

©G

lenc

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9G

lenc

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lgeb

ra 1

Lesson 3-4

Pre-

Act

ivit

yH

ow c

an e

qu

atio

ns

be

use

d t

o es

tim

ate

the

age

of a

n a

nim

al?

Rea

d th

e in

trod

uct

ion

to

Les

son

3-4

at

the

top

of p

age

142

in y

our

text

book

.

•W

rite

th

e eq

uat

ion

8 �

12a

�12

4 in

wor

ds.

Eig

ht

plu

s tw

elve

tim

es a

equ

als

on

e h

un

dre

d t

wen

ty-f

ou

r.•

How

man

y op

erat

ion

s ar

e in

volv

ed i

n t

he

equ

atio

n?

two

Rea

din

g t

he

Less

on

1.W

hat

doe

s th

e ph

rase

un

do

the

oper

atio

ns

mea

n t

o yo

u?

Giv

e an

exa

mpl

e.

Usi

ng

th

e o

pp

osi

te o

per

atio

ns

in t

he

op

po

site

ord

er u

nd

oes

th

eo

per

atio

ns;

sub

trac

tio

n u

nd

oes

ad

dit

ion

.

2.a.

If w

e u

ndo

ope

rati

ons

in r

ever

se o

f th

e or

der

of o

pera

tion

s,w

hat

ope

rati

ons

do w

e do

firs

t?ad

dit

ion

or

sub

trac

tio

n

b.

Wh

at o

pera

tion

s do

we

do l

ast?

mu

ltip

licat

ion

or

div

isio

n

3.S

upp

ose

you

wan

t to

sol

ve

�6.

a.W

hat

is

the

grou

pin

g sy

mbo

l in

th

e eq

uat

ion

�

6?th

e fr

acti

on

bar

b.

Wh

at i

s th

e fi

rst

step

in

sol

vin

g th

e eq

uat

ion

?M

ult

iply

eac

h s

ide

by 5

.

c.W

hat

is

the

nex

t st

ep i

n s

olvi

ng

the

equ

atio

n?

Su

btr

act

3 fr

om

eac

h s

ide.

4.W

rite

an

equ

atio

n f

or t

he

prob

lem

bel

ow.

Sev

entim

esk

min

usfiv

eeq

uals

nega

tive

fort

y-se

ven

7•

k�

5�

�47

Hel

pin

g Y

ou

Rem

emb

er

5.E

xpla

in w

hy

wor

kin

g ba

ckw

ard

is a

use

ful

stra

tegy

for

sol

vin

g eq

uat

ion

s.

Sam

ple

an

swer

:Yo

u c

an u

nd

o t

he

op

erat

ion

s to

get

bac

k to

th

e va

lue

of

the

vari

able

th

at w

ill m

ake

the

equ

atio

n t

rue.

Th

at v

alu

e is

th

e so

luti

on

.

x�

3�

5

x�

3�

5

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lenc

oe/M

cGra

w-H

ill16

0G

lenc

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lgeb

ra 1

Co

nse

cuti

ve In

teg

er P

rob

lem

sM

any

type

s of

pro

blem

s an

d pu

zzle

s in

volv

e th

e id

ea o

f co

nse

cuti

vein

tege

rs.K

now

ing

how

to

repr

esen

t th

ese

inte

gers

alg

ebra

ical

ly c

anh

elp

to s

olve

th

e pr

oble

m.

Fin

d f

our

con

secu

tive

od

d i

nte

gers

wh

ose

sum

is

�80

.

An

odd

in

tege

r ca

n b

e w

ritt

en a

s 2n

�1,

wh

ere

nis

an

y in

tege

r.If

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+ 1

is

the

firs

t od

d in

tege

r,th

en a

dd 2

to

get

the

nex

t la

rges

t od

din

tege

r,an

d so

on

.N

ow w

rite

an

equ

atio

n t

o so

lve

this

pro

blem

.(2

n�

1) �

(2n

�3)

�(2

n�

5) �

(2n

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��

80

Wri

te a

n e

qu

atio

n f

or e

ach

pro

ble

m.T

hen

sol

ve.

1.C

ompl

ete

the

solu

tion

to

the

prob

lem

in

th

e ex

ampl

e.

�23

,�21

,�19

,�17

2.F

ind

thre

e co

nse

cuti

ve e

ven

in

tege

rs w

hos

e su

m i

s 13

2.

2n�

(2n

�2)

�(2

n�

4) �

132;

n�

21;

42,4

4,46

3.F

ind

two

con

secu

tive

in

tege

rs w

hos

e su

m i

s 19

.

n�

(n�

1) �

19;

9,10

4.F

ind

two

con

secu

tive

in

tege

rs w

hos

e su

m i

s 10

0.

n�

(n�

1) �

100;

no

so

luti

on

5.T

he

less

er o

f tw

o co

nse

cuti

ve e

ven

in

tege

rs i

s 10

mor

e th

an

one-

hal

f th

e gr

eate

r.F

ind

the

inte

gers

.

2n�

10 �

(2n

�2)

;22

an

d 2

4

6.T

he

grea

ter

of t

wo

con

secu

tive

eve

n i

nte

gers

is

6 le

ss t

han

th

ree

tim

es t

he

less

er.F

ind

the

inte

gers

.

2n�

2 �

3(2n

) �

6;4,

6

7.F

ind

fou

r co

nse

cuti

ve i

nte

gers

su

ch t

hat

tw

ice

the

sum

of

the

two

grea

ter

inte

gers

exc

eeds

th

ree

tim

es t

he

firs

t by

91.

2[(n

�2)

�(n

�3)

] �

3n�

91;

81,8

2,83

,84

8.F

ind

a se

t of

fou

r co

nse

cuti

ve p

osit

ive

inte

gers

su

ch t

hat

th

e gr

eate

st i

nte

ger

in t

he

set

is t

wic

e th

e le

ast

inte

ger

in t

he

set.

n�

3 �

2n;

{3,4

,5,6

}

1 � 2

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-4

3-4

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Stu

dy G

uid

e a

nd I

nte

rven

tion

So

lvin

g E

qu

atio

ns

wit

h t

he

Var

iab

le o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-5

3-5

©G

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1G

lenc

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lgeb

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Lesson 3-5

Var

iab

les

on

Eac

h S

ide

To

solv

e an

equ

atio

n w

ith

th

e sa

me

vari

able

on

eac

h s

ide,

firs

t u

se t

he

Add

itio

n o

r th

e S

ubt

ract

ion

Pro

pert

y of

Equ

alit

y to

wri

te a

n e

quiv

alen

teq

uat

ion

th

at h

as t

he

vari

able

on

just

on

e si

de o

f th

e eq

uat

ion

.Th

en s

olve

th

e eq

uat

ion

.

Sol

ve 5

y�

8 �

3y�

12.

5y�

8�

3y�

125y

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2y�

8�

122y

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�12

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2y�

20

�

y�

10

Th

e so

luti

on i

s 10

.

20 � 22y � 2

Sol

ve �

11 �

3y�

8y�

1.

�11

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�8y

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y�

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y

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Th

e so

luti

on i

s �

1.

1 � 11

1 � 11

11y

� 11�

12�11

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Sol

ve e

ach

eq

uat

ion

.Th

en c

hec

k y

our

solu

tion

.

1.6

�b

�5b

�30

2.5y

�2y

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3.5x

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�10

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no

so

luti

on

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5.1.

2x�

4.3

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1 �

x 6.

4.4s

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2 �

8.8s

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8

10�

1

7.b

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x�

8 �

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12.3

y�

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8

35

all n

um

ber

s

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4 �

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7x�

614

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15.2

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n�

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no

so

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32 � 9

3 � 52 � 5

1 � 22 � 31 � 5

1 � 43 � 4

1 � 81 � 2

20 � 11

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Gro

up

ing

Sym

bo

lsW

hen

sol

vin

g eq

uat

ion

s th

at c

onta

in g

rou

pin

g sy

mbo

ls,f

irst

use

the

Dis

trib

uti

ve P

rope

rty

to e

lim

inat

e gr

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ng

sym

bols

.Th

en s

olve

.

Sol

ve 4

(2a

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��

10(a

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.

4(2a

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��

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Orig

inal

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atio

n

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Pro

pert

y

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plify

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4 t

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plify

.

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ivid

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8.

a�

3S

impl

ify.

Th

e so

luti

on i

s 3.

Sol

ve e

ach

eq

uat

ion

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en c

hec

k y

our

solu

tion

.

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3(x

�5)

�3(

x�

1)2.

2(7

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) �

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a�

1) �

5 �

3a�

2

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all n

um

ber

s

4.75

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6

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2c�

2)8.

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5(p

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p�

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6

2n

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olu

tio

n�

12

10.4

(b�

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11.1

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�

32

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13.

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�2k

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10 �

k15

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w�

1)

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(n�

1) �

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[2 �

3(y

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] �

2218

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r�

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4(2

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74

1

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3(x

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y�

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54 � 1818

a� 18S

tudy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

So

lvin

g E

qu

atio

ns

wit

h t

he

Var

iab

le o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

3-5

3-5

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Skil

ls P

ract

ice

So

lvin

g E

qu

atio

ns

wit

h t

he

Var

iab

le o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-5

3-5

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3G

lenc

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lgeb

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Lesson 3-5

Ju

stif

y ea

ch s

tep

.

1.4k

�3

�2k

�5

4k�

3 �

2k�

2k�

5 �

2ka.

Su

btr

act

2kfr

om

eac

h s

ide.

2k�

3 �

5b

.S

imp

lify.

2k�

3 �

3 �

5 �

3c.

Ad

d 3

to

eac

h s

ide.

2k�

8d

.S

imp

lify.

�e.

Div

ide

each

sid

e by

2.

k�

4f.

Sim

plif

y.

2.2(

8u�

2) �

3(2u

�7)

16u

�4

�6u

�21

a.D

istr

ibu

tive

Pro

per

ty

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Sim

plif

y.

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e.

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plif

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ide

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plif

y.

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ve e

ach

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uat

ion

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en c

hec

k y

our

solu

tion

.

3.2m

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434.

2h�

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h�

1725

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n

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l nu

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214

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r �

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v�

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27 � 2

7 � 85 � 8

1 � 22 � 3

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1 � 21 � 2

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Sol

ve e

ach

eq

uat

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.Th

en c

hec

k y

our

solu

tion

.

1.5x

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�13

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22.

�4c

�11

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3.1

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14 �

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no

so

luti

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4 �

w)

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13.

t�

t�

3 �

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f�

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3 �

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x�

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.(c

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c�

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20.

(2m

�16

) �

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l nu

mb

ers

21.3

(d�

8) �

5 �

9(d

�2)

�1

�8

22.2

(a�

8) �

7 �

5(a

�2)

�3a

�19

23.T

wo

thir

ds o

f a

nu

mbe

r re

duce

d by

11

is e

qual

to

4 m

ore

than

th

e n

um

ber.

Fin

d th

en

um

ber.

�45

24.F

ive

tim

es t

he

sum

of

a n

um

ber

and

3 is

th

e sa

me

as 3

mu

ltip

lied

by

1 le

ss t

han

tw

ice

the

nu

mbe

r.W

hat

is

the

nu

mbe

r?18

25.N

UM

BER

TH

EORY

Tri

plin

g th

e gr

eate

r of

tw

o co

nsec

utiv

e ev

en i

nteg

ers

give

s th

e sa

me

resu

lt a

s su

btra

ctin

g 10

fro

m t

he

less

er e

ven

in

tege

r.W

hat

are

th

e in

tege

rs?

�8,

�6

26.G

EOM

ETRY

Th

e fo

rmu

la f

or t

he

peri

met

er o

f a

rect

angl

e is

P�

2��

2w,w

her

e �

isth

e le

ngt

h a

nd

wis

th

e w

idth

.A r

ecta

ngl

e h

as a

per

imet

er o

f 24

in

ches

.Fin

d it

sdi

men

sion

s if

its

len

gth

is

3 in

ches

gre

ater

th

an i

ts w

idth

.4.

5 in

.by

7.5

in.

1 � 31 � 9

1 � 4h � 2

1 � 4

1 � 61 � 3

3 � 4g � 6

1 � 2

1 � 83 � 4

5 � 61 � 2

1 � 62 � 3

3 � 25 � 2

5 � 6

1 � 23 � 4

1 � 2

1 � 3

Pra

ctic

e (

Ave

rag

e)

So

lvin

g E

qu

atio

ns

wit

h t

he

Var

iab

le o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-5

3-5



Readin

g t

o L

earn

Math

em

ati

csS

olv

ing

Eq

uat

ion

s w

ith

th

e V

aria

ble

on

Eac

h S

ide

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-5

3-5

©G

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5G

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lgeb

ra 1

Lesson 3-5

Pre-

Act

ivit

yH

ow c

an a

n e

qu

atio

n b

e u

sed

to

det

erm

ine

wh

en t

wo

pop

ula

tion

sar

e eq

ual

?

Rea

d th

e in

trod

uct

ion

to

Les

son

3-5

at

the

top

of p

age

149

in y

our

text

book

.

In t

he

equ

atio

n 1

2 �

7.6x

�6

�8x

,wh

at d

o 7.

6xan

d 8x

repr

esen

t?

7.6x

rep

rese

nts

th

e in

crea

se (

in m

illio

ns)

in t

he

nu

mb

er o

fm

ale

Inte

rnet

use

rs,a

nd

8x

rep

rese

nts

th

e in

crea

se (

inm

illio

ns)

in t

he

nu

mb

er o

f fe

mal

e In

tern

et u

sers

.

Rea

din

g t

he

Less

on

1.S

upp

ose

you

wan

t to

hel

p a

frie

nd

solv

e 6k

�7

�3k

�8.

Wh

at w

ould

you

adv

ise

her

to

do f

irst

? W

hy?

Su

btr

act

3kfr

om

eac

h s

ide;

afte

r sh

e d

oes

th

at a

nd

sim

plif

ies,

all o

f th

eva

riab

les

will

be

on

th

e le

ft s

ide.

2.W

hen

sol

vin

g 2(

3x�

4)�

3(x

�5)

,wh

y is

it

hel

pfu

l fi

rst

to u

se t

he

Dis

trib

uti

ve P

rope

rty

to r

emov

e th

e gr

oupi

ng

sym

bols

?

On

ce y

ou

hav

e re

mov

ed t

he

gro

up

ing

sym

bo

ls,y

ou

can

tel

l wh

at y

ou

nee

dto

add

or

sub

trac

t to

eac

h s

ide

to g

et a

ll o

f th

e va

riab

les

on

on

e si

de.

3.O

n a

qu

iz,J

ason

sol

ved

thre

e eq

uat

ion

s.H

is t

each

er s

aid

all

the

wor

k w

as c

orre

ct,b

ut

she

aske

d h

im t

o w

rite

sh

ort

sen

ten

ces

to t

ell

wh

at t

he

solu

tion

s w

ere.

In w

hat

fol

low

s,yo

u s

ee t

he

last

equ

atio

n i

n h

is w

ork

for

each

equ

atio

n.W

rite

sen

ten

ces

to d

escr

ibe

the

solu

tion

s.

a.x

��

4T

he

solu

tio

n is

�4.

b.

6m�

6mA

ll n

um

ber

s ar

e so

luti

on

s.c.

12 �

37T

her

e ar

e n

o s

olu

tio

ns.

4.In

Qu

esti

on 3

,on

e of

th

e eq

uat

ion

s Ja

son

sol

ved

was

an

ide

nti

ty.W

hic

h e

quat

ion

was

it?

Exp

lain

how

you

kn

ow.

Th

e o

ne

for

wh

ich

th

e la

st s

tep

was

6m

�6m

;th

e ex

pre

ssio

ns

on

th

e le

ftan

d r

igh

t si

des

are

th

e sa

me.

Hel

pin

g Y

ou

Rem

emb

er

5.A

n e

quat

ion

wit

h v

aria

bles

is

an i

den

tity

wh

en t

he

equ

atio

n i

s al

way

s tr

ue.

In o

ther

wor

ds,t

he

expr

essi

ons

on t

he

left

an

d ri

ght

side

s al

way

s h

ave

the

sam

e va

lue.

Loo

k u

pth

e w

ord

iden

tity

in t

he

dict

ion

ary.

Wri

te a

ll t

he

defi

nit

ion

s th

at a

re s

imil

ar t

o th

em

ath

emat

ical

def

init

ion

.S

ee s

tud

ents

’wo

rk.

©G

lenc

oe/M

cGra

w-H

ill16

6G

lenc

oe A

lgeb

ra 1

Iden

titi

esA

n e

quat

ion

th

at i

s tr

ue

for

ever

y va

lue

of t

he

vari

able

is

call

ed a

nid

enti

ty.W

hen

you

try

to

solv

e an

ide

nti

ty,y

ou e

nd

up

wit

h a

stat

emen

t th

at i

s al

way

s tr

ue.

Her

e is

an

exa

mpl

e.

Sol

ve 8

�(5

�6x

) �

3(1

�2x

).

8 �

(5 �

6x)

�3(

1 �

2x)

8 �

5 �

(�6x

)�

3(1

�2x

)

8 �

5 �

6x�

3 �

6x

3 �

6x�

3 �

6x

Sta

te w

het

her

eac

h e

qu

atio

n i

s an

id

enti

ty.I

f it

is

not

,fin

d i

ts s

olu

tion

.

1.2(

2 �

3x)

�3(

3 �

x) �

42.

5(m

�1)

�6

�3(

4 �

m)

�(2

m�

1)

x�

�1

iden

tity

3.(5

t�

9) �

(3t

�13

) �

2(11

�t)

4.14

�(6

�3c

) �

4c �

c

iden

tity

no

so

luti

on

5.3y

�2(

y�

19)

�9y

�3(

9 �

y)6.

3(3h

�1)

�4(

h�

3)

y�

�1

h�

3

7.U

se t

he

tru

e eq

uat

ion

3x

�2

�3x

�2

to c

reat

e an

ide

nti

ty o

f yo

ur

own

.

Sam

ple

an

swer

: 6x

�4

�2(

3x�

2)

8.U

se t

he

fals

e eq

uat

ion

1 �

2 to

cre

ate

an e

quat

ion

wit

h n

o so

luti

on.

Sam

ple

an

swer

: 2x

�1

�2x

�2

9.C

reat

e an

equ

atio

n w

hos

e so

luti

on i

s x

�3.

Sam

ple

an

swer

: 3x

�2(

x�

1) �

20

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-5

3-5

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

Rat

ios

and

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-6

3-6

©G

lenc

oe/M

cGra

w-H

ill16

7G

lenc

oe A

lgeb

ra 1

Lesson 3-6

Rat

ios

and

Pro

po

rtio

ns

A r

atio

is a

com

pari

son

of

two

nu

mbe

rs b

y di

visi

on.T

he

rati

o

of x

to y

can

be

expr

esse

d as

xto

y,x

:yor

.R

atio

s ar

e u

sual

ly e

xpre

ssed

in

sim

ples

t fo

rm.

An

equ

atio

n s

tati

ng

that

tw

o ra

tios

are

equ

al i

s ca

lled

a p

rop

orti

on.T

o de

term

ine

wh

eth

ertw

o ra

tios

for

m a

pro

port

ion

,exp

ress

bot

h r

atio

s in

sim

ples

t fo

rm o

r ch

eck

cros

s pr

odu

cts.

x � y

Det

erm

ine

wh

eth

er t

he

rati

os

and

fo

rm a

pro

por

tion

.

�w

hen

exp

ress

ed i

n s

impl

est

form

.

�w

hen

exp

ress

ed i

n s

impl

est

form

.

Th

e ra

tios

an

d fo

rm a

pro

port

ion

beca

use

th

ey a

re e

qual

wh

en e

xpre

ssed

in

sim

ples

t fo

rm.

12 � 1824 � 36

2 � 312 � 18

2 � 324 � 36

12 � 1824 � 36

Use

cro

ss p

rod

uct

s to

det

erm

ine

wh

eth

er

and

fo

rm a

pro

por

tion

.

�W

rite

the

prop

ortio

n.

10(4

5) �

18(2

5)C

ross

pro

duct

s

450

�45

0S

impl

ify.

Th

e cr

oss

prod

uct

s ar

e eq

ual

,so

�.

Sin

ce t

he

rati

os a

re e

qual

,th

ey f

orm

apr

opor

tion

.

25 � 4510 � 18

25 � 4510 � 18

25 � 4510 � 18

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Use

cro

ss p

rod

uct

s to

det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

form

s a

pro

por

tion

.

1.,

2.,

3.,

yes

no

no

4.,

5.,

6.,

no

no

yes

7.,

8.,

9.,

yes

yes

yes

10.2

:3,2

0:3

011

.5 t

o 9,

25 t

o 45

12.

,

yes

yes

yes

13.5

:5,3

0:2

014

.18

to 2

4,50

to

7515

.100

:75,

44:3

3

no

no

yes

16.

,17

.,

18.

,

yes

yes

yes

0.45

� 0.9

0.1

� 0.2

6 � 81.

5�2

1 � 200.

05�

1

9 � 872 � 64

20 � 3014 � 21

9 � 1215 � 20

5� 10

00.

1�2

12 � 274 � 9

3 � 1612 � 32

15 � 2025 � 36

25 � 4910 � 20

10 � 155 � 8

16 � 321 � 2

©G

lenc

oe/M

cGra

w-H

ill16

8G

lenc

oe A

lgeb

ra 1

Solv

e Pr

op

ort

ion

sIf

a p

ropo

rtio

n in

volv

es a

var

iabl

e,yo

u ca

n us

e cr

oss

prod

ucts

to

solv

e

the

prop

orti

on.I

n t

he

prop

orti

on

�,x

and

13 a

re c

alle

d ex

trem

esan

d 5

and

10 a

re

calle

d m

ean

s.In

a p

ropo

rtio

n,th

e pr

oduc

t of

the

ext

rem

es is

equ

al t

o th

e pr

oduc

t of

the

mea

ns.

Mea

ns-

Ext

rem

es P

rop

erty

of

Pro

po

rtio

ns

For

any

num

bers

a,

b, c

,an

d d,

if

�,

then

ad

�bc

.

Sol

ve

�.

�O

rigin

al p

ropo

rtio

n

13(x

) �

5(10

)C

ross

pro

duct

s

13x

�50

Sim

plify

.

�D

ivid

e ea

ch s

ide

by 1

3.

x�

3S

impl

ify.

Th

e so

luti

on i

s 3

.

Sol

ve e

ach

pro

por

tion

.

1.�

�12

2.�

3.�

10

4.�

25.

�12

6.�

1

7.�

268.

�9.

�15

10.

�14

11.

�n

o s

olu

tio

n12

.�

�2

13.

�68

14.

�n

o s

olu

tio

n15

.�

6

Use

a p

rop

orti

on t

o so

lve

each

pro

ble

m.

16. M

OD

ELS

To

mak

e a

mod

el o

f th

e G

uad

elou

pe R

iver

bed

,Her

mie

use

d 1

inch

of

clay

for

5 m

iles

of

the

rive

r’s

actu

al l

engt

h.H

is m

odel

riv

er w

as 5

0 in

ches

lon

g.H

ow l

ong

is t

he

Gu

adel

oupe

Riv

er?

250

mi

17.E

DU

CA

TIO

NJo

sh f

inis

hed

24

mat

h p

robl

ems

in o

ne

hou

r.A

t th

at r

ate,

how

man

yh

ours

wil

l it

tak

e h

im t

o co

mpl

ete

72 p

robl

ems?

3 h

12 � 92

� w

�6

24 � k12 � k

15 � 3a

�8

�12

�y

�8

3 �

y�

412 � x

1.5

�x

4 � 124

� b�

2

p � 245 � 8

1 � 218 � 3

3 � d18 � 54

9� y

�1

3 � 63x � 21

8 � x4 � 6

3 � 4x

�1

�4

0.5

�x

0.1

�2

3 � 55 � 3

1 � t2 � 8

�3

�x

11 � 13

11 � 13

50 � 1313

x� 13

10 � 13x � 5

10 � 13x � 5

c � da � b

10 � 13x � 5

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Rat

ios

and

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-6

3-6

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

Rat

ios

and

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-6

3-6

©G

lenc

oe/M

cGra

w-H

ill16

9G

lenc

oe A

lgeb

ra 1

Lesson 3-6

Use

cro

ss p

rod

uct

s to

det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

form

s a

pro

por

tion

.W

rite

yes

or n

o.

1.,

yes

2.,

no

3.,

yes

4.,

yes

5.,

no

6.,

yes

7.,

yes

8.,

no

Sol

ve e

ach

pro

por

tion

.If

nec

essa

ry,r

oun

d t

o th

e n

eare

st h

un

dre

dth

.

9.�

710

.�

15

11.

�6

12.

�18

13.

�10

14.

�3

15.

�21

16.

�18

17.

�8

18.

�63

19.

�42

20.

�44

21.

�13

22.

�48

23.

�16

24.

�60

25.B

OA

TIN

GH

ue’

s bo

at u

sed

5 ga

llon

s of

gas

olin

e in

4 h

ours

.At

this

rat

e,h

ow m

any

gall

ons

of g

asol

ine

wil

l th

e bo

at u

se i

n 1

0 h

ours

?12

.5 g

al

11 � 3022 � x

s � 844 � 21

20 � g5 � 12

27 � 399 � c

n � 6011 � 15

30 � m10 � 14

1 � 97 � b

6 � f42 � 56

y � 696 � 23

36 � s12 � 7

35 � 215 � e

3 � 56 � z

1 � 63 � a

15 � 109 � g

3 � 95 � b

2 � 141 � a

50 � 8512 � 17

21 � 983 � 14

26 � 3813 � 19

42 � 907 � 16

72 � 818 � 9

24 � 286 � 7

7 � 115 � 9

20 � 254 � 5

©G

lenc

oe/M

cGra

w-H

ill17

0G

lenc

oe A

lgeb

ra 1

Use

cro

ss p

rod

uct

s to

det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

form

s a

pro

por

tion

.W

rite

yes

or n

o.

1.,

no

2.,

no

3.,

yes

4.,

yes

5.,

yes

6.,

yes

7.,

yes

8.,

no

9.,

no

Sol

ve e

ach

pro

por

tion

.If

nec

essa

ry,r

oun

d t

o th

e n

eare

st h

un

dre

dth

.

10.

�9

11.

�68

12.

�5

13.

�7

14.

�18

15.

�16

16.

�12

17.

�77

18.

�1

19.

�12

220

.�

2421

.�

7

22.

�10

23.

�3

24.

�3

25.

�1

26.

�2.

8827

.�

1.02

28.

�7

29.

�2

30.

�5

31.

�32

.�

333

.�

4

34.P

AIN

TIN

GY

sidr

a pa

ints

a r

oom

th

at h

as 4

00 s

quar

e fe

et o

f w

all

spac

e in

2h

ours

.At

this

rat

e,h

ow l

ong

wil

l it

tak

e h

er t

o pa

int

a ro

om t

hat

has

720

squ

are

feet

of

wal

lsp

ace?

4h

35.V

AC

ATI

ON

PLA

NS

Wal

ker

is p

lan

nin

g a

sum

mer

vac

atio

n.H

e w

ants

to

visi

t P

etri

fied

Nat

ion

al F

ores

t an

d M

eteo

r C

rate

r,A

rizo

na,

the

50,0

00-y

ear-

old

impa

ct s

ite

of a

lar

gem

eteo

r.O

n a

map

wit

h a

sca

le w

her

e 2

inch

es e

qual

s 75

mil

es,t

he

two

area

s ar

e ab

out

1in

ches

apa

rt.W

hat

is

the

dist

ance

bet

wee

n P

etri

fied

Nat

ion

al F

ores

t an

d M

eteo

r

Cra

ter?

abo

ut

56.2

5 m

i

1 � 2

1 � 2

1 � 24 � 7x

�2

�6

3 � 75 � 7

r�

2�

72 � 3

x�

1�

45 � 12

2 � 4m

�1

�8

2� y

�6

3 � 1214 � 6

7� a

�4

3� 0.

516 � n

12 � b3

� 0.72

7� 1.

61v

� 0.23

3 � 45 � 8

m � 63 � 5

5 � 63 � q

2 � 78 � c

7 � 9

2 � a14 � 49

6 � 4g � 16

12 � h6 � 61

z � 173 � 51

35 � x5 � 11

10 � 602 � y

48 � 9y � 3

27 � 162

3 � u4 � w

28 � 49

k � 740 � 56

34 � 23v � 46

30 � 545 � a

3.9

� 0.9

7.6

� 1.8

2.9

� 2.4

1.7

� 1.2

7.14

� 10.9

23.

4� 5.

2

1 � 61.

5�9

72 � 818 � 9

108

� 9912 � 11

36 � 4818 � 24

15 � 663 � 11

52 � 487 � 6

Pra

ctic

e (

Ave

rag

e)

Rat

ios

and

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-6

3-6



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csR

atio

s an

d P

rop

ort

ion

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-6

3-6

©G

lenc

oe/M

cGra

w-H

ill17

1G

lenc

oe A

lgeb

ra 1

Lesson 3-6

Pre-

Act

ivit

yH

ow a

re r

atio

s u

sed

in

rec

ipes

?

Rea

d th

e in

trod

uct

ion

to

Les

son

3-6

at

the

top

of p

age

155

in y

our

text

book

.

•H

ow m

any

serv

ings

of

hon

ey f

roze

n y

ogu

rt a

re m

ade

by t

his

rec

ipe?

4 se

rvin

gs

•H

ow m

any

reci

pes

wou

ld b

e n

eede

d to

mak

e en

ough

hon

ey f

roze

n y

ogu

rtfo

r al

l th

e st

ude

nts

in

you

r cl

ass?

See

stu

den

ts’w

ork

.

Rea

din

g t

he

Less

on

1.C

ompl

ete

the

foll

owin

g se

nte

nce

.

A r

atio

is

a co

mpa

riso

n o

f tw

o n

um

bers

by

.

2.D

escr

ibe

two

way

s to

dec

ide

wh

eth

er t

he

sen

ten

ce

�is

a p

ropo

rtio

n.

Exp

ress

th

e ra

tio

s in

sim

ple

st f

orm

to

see

if t

hey

are

eq

ual

.Ch

eck

to s

eew

het

her

th

e cr

oss

pro

du

cts

are

equ

al.

3.F

or e

ach

pro

port

ion

,tel

l w

hat

th

e ex

trem

es a

re a

nd

wh

at t

he

mea

ns

are.

a.�

Ext

rem

es:

Mea

ns:

b.

�E

xtre

mes

:M

ean

s:

4.A

jet

flyi

ng

at a

ste

ady

spee

d tr

avel

ed 8

25 m

iles

in

2 h

ours

.If

you

sol

ved

the

prop

orti

on

�,w

hat

wou

ld t

he

answ

er t

ell

you

abo

ut

the

jet?

ho

w f

ar t

he

jet

trav

eled

in 1

.5 h

Hel

pin

g Y

ou

Rem

emb

er

5.W

rite

how

you

wou

ld e

xpla

in s

olvi

ng

a pr

opor

tion

to

a fr

ien

d w

ho

mis

sed

Les

son

3-6

.

Use

cro

ss p

rod

uct

s.W

rite

an

eq

uat

ion

wit

h t

he

pro

du

ct o

f th

e ex

trem

eso

n t

he

left

sid

e an

d t

he

pro

du

ct o

f th

e m

ean

s o

n t

he

rig

ht

sid

e.T

hen

solv

e th

is s

eco

nd

eq

uat

ion

.

x� 1.

582

5�

2

8 an

d 1

26

and

16

12 � 166 � 8

35 a

nd

614

an

d 1

56 � 15

14 � 35

8 � 202 � 5div

isio

n

©G

lenc

oe/M

cGra

w-H

ill17

2G

lenc

oe A

lgeb

ra 1

An

gle

s o

f a

Tria

ng

leIn

geo

met

ry,m

any

stat

emen

ts a

bou

t ph

ysic

al s

pace

are

pro

ven

to

betr

ue.

Su

ch s

tate

men

ts a

re c

alle

d th

eore

ms.

Her

e ar

e tw

o ex

ampl

es o

fge

omet

ric

theo

rem

s.

a.T

he

sum

of

the

mea

sure

s of

th

e an

gles

of

a tr

ian

gle

is 1

80°.

b.

If t

wo

side

s of

a t

rian

gle

hav

e eq

ual

mea

sure

,th

en t

he

two

angl

esop

posi

te t

hos

e si

des

also

hav

e eq

ual

mea

sure

.

For

eac

h o

f th

e tr

ian

gles

,wri

te a

n e

qu

atio

n a

nd

th

en s

olve

for

x.(

A t

ick

mar

k o

ntw

o or

mor

e si

des

of

a tr

ian

gle

ind

icat

es t

hat

th

e si

des

hav

e eq

ual

mea

sure

.)

1.x

�60

2.

x�

45

3.x

�45

4.

x�

20

5.x

�22

.5

6.x

�10

7.x

�33

8.

x�

100

9.x

�60

10

.x

�50

11.T

wo

angl

es o

f a

tria

ngl

e h

ave

the

sam

e12

.Th

e m

easu

re o

f on

e an

gle

of a

tri

angl

e is

m

easu

re.T

he

sum

of

the

mea

sure

s of

tw

ice

the

mea

sure

of

a se

con

d an

gle.

Th

e th

ese

angl

es i

s on

e-h

alf

the

mea

sure

of

mea

sure

of

the

thir

d an

gle

is 1

2 le

ss t

han

th

e th

ird

angl

e.F

ind

the

mea

sure

s of

th

e su

m o

f th

e ot

her

tw

o.F

ind

the

the

angl

es o

f th

e tr

ian

gle.

mea

sure

s of

th

e an

gles

of

the

tria

ngl

e.30

,30

,12

064

,32

,84

x2x

30°

x

40°

x

x �

15°

3 x

x �

30°

90°

4 x

5x

5x

2xx

x �

30°

x5x

� 1

0°

90°

x

90°

45°

x70

°

50°

x

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-6

3-6



Stu

dy G

uid

e a

nd I

nte

rven

tion

Per

cen

t o

f C

han

ge

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-7

3-7

©G

lenc

oe/M

cGra

w-H

ill17

3G

lenc

oe A

lgeb

ra 1

Lesson 3-7

Perc

ent

of

Ch

ang

eW

hen

an

in

crea

se o

r de

crea

se i

n a

n a

mou

nt

is e

xpre

ssed

as

ape

rcen

t,th

e pe

rcen

t is

cal

led

the

per

cen

t of

ch

ange

.If

the

new

nu

mbe

r is

gre

ater

th

an t

he

orig

inal

nu

mbe

r,th

e pe

rcen

t of

ch

ange

is

a p

erce

nt

of i

ncr

ease

.If

the

new

nu

mbe

r is

les

sth

an t

he

orig

inal

nu

mbe

r,th

e pe

rcen

t of

ch

ange

is

the

per

cen

t of

dec

reas

e.

Fin

d t

he

per

cen

t of

in

crea

se.

orig

inal

:48

new

:60

Fir

st,s

ubt

ract

to

fin

d th

e am

oun

t of

incr

ease

.Th

e am

oun

t of

in

crea

se i

s 60

�48

�12

.T

hen

fin

d th

e pe

rcen

t of

in

crea

se b

y u

sin

gth

e or

igin

al n

um

ber,

48,a

s th

e ba

se.

�P

erce

nt p

ropo

rtio

n

12(1

00)

�48

(r)

Cro

ss p

rodu

cts

1200

�48

rS

impl

ify.

�D

ivid

e ea

ch s

ide

by 4

8.

25 �

rS

impl

ify.

Th

e pe

rcen

t of

in

crea

se i

s 25

%.

48r

� 4812

00�

48

r� 10

012 � 48

Fin

d t

he

per

cen

t of

dec

reas

e.or

igin

al:3

0n

ew:2

2

Fir

st,s

ubt

ract

to

fin

d th

e am

oun

t of

decr

ease

.Th

e am

oun

t of

dec

reas

e is

30

�22

�8.

Th

en f

ind

the

perc

ent

of d

ecre

ase

by u

sin

gth

e or

igin

al n

um

ber,

30,a

s th

e ba

se.

�P

erce

nt p

ropo

rtio

n

8(10

0) �

30(r

)C

ross

pro

duct

s

800

�30

rS

impl

ify.

�D

ivid

e ea

ch s

ide

by 3

0.

26�

rS

impl

ify.

Th

e pe

rcen

t of

dec

reas

e is

26

%,o

r ab

out

27%

.

2 � 3

2 � 3

30r

� 3080

0� 30

r� 10

08 � 30

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Sta

te w

het

her

eac

h p

erce

nt

of c

han

ge i

s a

per

cen

t of

in

crea

se o

r a

per

cen

t of

dec

reas

e.T

hen

fin

d e

ach

per

cen

t of

ch

ange

.Rou

nd

to

the

nea

rest

wh

ole

per

cen

t.

1.or

igin

al:5

02.

orig

inal

:90

3.or

igin

al:4

5n

ew:8

0n

ew:1

00n

ew:2

0in

crea

se;

60%

incr

ease

:11

%d

ecre

ase;

56%

4.or

igin

al:7

7.5

5.or

igin

al:1

406.

orig

inal

:135

new

:62

new

:150

new

:90

dec

reas

e;20

%in

crea

se:

7%d

ecre

ase;

33%

7.or

igin

al:1

208.

orig

inal

:90

9.or

igin

al:2

7.5

new

:180

new

:270

new

:25

incr

ease

;50

%in

crea

se:

200%

dec

reas

e;9%

10.o

rigi

nal

:84

11.o

rigi

nal

:12.

512

.ori

gin

al:2

50n

ew:9

8n

ew:1

0n

ew:5

00in

crea

se;

17%

dec

reas

e:20

%in

crea

se;

100%

©G

lenc

oe/M

cGra

w-H

ill17

4G

lenc

oe A

lgeb

ra 1

Solv

e Pr

ob

lem

sD

isco

un

ted

pric

es a

nd

pric

es i

ncl

udi

ng

tax

are

appl

icat

ion

s of

per

cen

tof

ch

ange

.Dis

cou

nt

is t

he

amou

nt

by w

hic

h t

he

regu

lar

pric

e of

an

ite

m i

s re

duce

d.T

hu

s,th

e di

scou

nte

d pr

ice

is a

n e

xam

ple

of p

erce

nt

of d

ecre

ase.

Sal

es t

ax i

s am

oun

t th

at i

s ad

ded

to t

he

cost

of

an i

tem

,so

the

pric

e in

clu

din

g ta

x is

an

exa

mpl

e of

per

cen

t of

in

crea

se.

A c

oat

is o

n s

ale

for

25%

off

th

e or

igin

al p

rice

.If

the

orig

inal

pri

ceof

th

e co

at i

s $7

5,w

hat

is

the

dis

cou

nte

d p

rice

?

Th

e di

scou

nt

is 2

5% o

f th

e or

igin

al p

rice

.

25%

of

$75

�0.

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he

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d t

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al p

rice

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each

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com

pu

te t

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dis

cou

nt

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ce b

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uti

ng

the

tax.

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wo

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ty c

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are:

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20

10.V

IDEO

ST

he

orig

inal

sel

lin

g pr

ice

of a

new

spo

rts

vide

o w

as $

65.0

0.D

ue

to t

he

dem

and

the

pric

e w

as i

ncr

ease

d to

$87

.75.

Wh

at w

as t

he

perc

ent

of i

ncr

ease

ove

r th

e or

igin

alpr

ice?

35%

11.S

CH

OO

LA

hig

h s

choo

l pa

per

incr

ease

d it

s sa

les

by 7

5% w

hen

it

ran

an

iss

ue

feat

uri

ng

a co

nte

st t

o w

in a

cla

ss p

arty

.Bef

ore

the

con

test

iss

ue,

10%

of

the

sch

ool’s

800

stu

den

tsbo

ugh

t th

e pa

per.

How

man

y st

ude

nts

bou

ght

the

con

test

iss

ue?

140

stu

den

ts

12.B

ASE

BA

LLB

aseb

all

tick

ets

cost

$15

for

gen

eral

adm

issi

on o

r $2

0 fo

r bo

x se

ats.

Th

esa

les

tax

on e

ach

tic

ket

is 8

%,a

nd

the

mu

nic

ipal

tax

on

eac

h t

icke

t is

an

add

itio

nal

10%

of t

he

base

pri

ce.W

hat

is

the

fin

al c

ost

of e

ach

typ

e of

tic

ket?

$17.

70;

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60

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Per

cen

t o

f C

han

ge

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-7

3-7

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Skil

ls P

ract

ice

Per

cen

t o

f C

han

ge

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

E__

____

____

__P

ER

IOD

____

_

3-7

3-7

©G

lenc

oe/M

cGra

w-H

ill17

5G

lenc

oe A

lgeb

ra 1

Lesson 3-7

Sta

te w

het

her

eac

h p

erce

nt

of c

han

ge i

s a

per

cen

t of

in

crea

se o

r a

per

cen

t of

dec

reas

e.T

hen

fin

d e

ach

per

cen

t of

ch

ange

.Rou

nd

to

the

nea

rest

wh

ole

per

cen

t.

1.or

igin

al:2

52.

orig

inal

:50

new

:10

new

:75

dec

reas

e;60

%in

crea

se;

50%

3.or

igin

al:5

54.

orig

inal

:25

new

:50

new

:28

dec

reas

e;9%

incr

ease

;12

%

5.or

igin

al:5

06.

orig

inal

:90

new

:30

new

:95

dec

reas

e;40

%in

crea

se;

6%

7.or

igin

al:4

88.

orig

inal

:60

new

:60

new

:45

incr

ease

;25

%d

ecre

ase;

25%

Fin

d t

he

tota

l p

rice

of

each

ite

m.

9.dr

ess:

$69.

0010

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der:

$14.

50ta

x:5%

tax:

7%$7

2.45

$15.

52

11.h

ardc

over

boo

k:$2

8.95

12.g

roce

ries

:$47

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tax:

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69$4

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ille

r pa

per:

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oes:

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cou

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rice

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ite

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17.b

ackp

ack:

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2518

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itor

:$15

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disc

oun

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00$7

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irt:

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30

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aker

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75$5

6.10

©G

lenc

oe/M

cGra

w-H

ill17

6G

lenc

oe A

lgeb

ra 1

Sta

te w

het

her

eac

h p

erce

nt

of c

han

ge i

s a

per

cen

t of

in

crea

se o

r a

per

cen

t of

dec

reas

e.T

hen

fin

d e

ach

per

cen

t of

ch

ange

.Rou

nd

to

the

nea

rest

wh

ole

per

cen

t.

1.or

igin

al:1

82.

orig

inal

:140

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igin

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ecre

ase;

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ease

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%in

crea

se;

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igin

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05.

orig

inal

:76

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igin

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5n

ew:6

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se;

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dec

reas

e;21

%d

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ase;

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7.or

igin

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58.

orig

inal

:98.

69.

orig

inal

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new

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new

:65.

7in

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se;

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dec

reas

e;35

%in

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se;

12%

Fin

d t

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tota

l p

rice

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oncr

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ks:$

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b:$2

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.00

tax:

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Fin

d t

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cou

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d p

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ry c

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pute

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me:

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t:45

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1.66

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$13.

74

Fin

d t

he

fin

al p

rice

of

each

ite

m.

22.t

elev

isio

n:$

375.

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.DV

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laye

r:$2

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nte

r:$2

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scou

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25%

disc

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t:20

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nt:

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tax:

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tax:

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$298

.13

$230

.26

$188

.32

25.I

NV

ESTM

ENTS

Th

e pr

ice

per

shar

e of

an

in

tern

et-r

elat

ed s

tock

dec

reas

ed f

rom

$90

per

shar

e to

$36

per

sh

are

earl

y in

200

1.B

y w

hat

per

cen

t di

d th

e pr

ice

of t

he

stoc

kde

crea

se?

60%

26.H

EATI

NG

CO

STS

Cu

stom

ers

of a

uti

lity

com

pan

y re

ceiv

ed n

otic

es i

n t

hei

r m

onth

ly b

ills

that

hea

tin

g co

sts

for

the

aver

age

cust

omer

had

in

crea

sed

125%

ove

r la

st y

ear

beca

use

of a

n u

nu

sual

ly s

ever

e w

inte

r.In

Jan

uar

y of

las

t ye

ar,t

he

Gar

cia’

s pa

id $

120

for

hea

tin

g.W

hat

sh

ould

th

ey e

xpec

t to

pay

th

is J

anu

ary

if t

hei

r bi

ll i

ncr

ease

d by

125

%?

$270

Pra

ctic

e (

Ave

rag

e)

Per

cen

t o

f C

han

ge

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-7

3-7



Readin

g t

o L

earn

Math

em

ati

csP

erce

nt

of

Ch

ang

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-7

3-7

©G

lenc

oe/M

cGra

w-H

ill17

7G

lenc

oe A

lgeb

ra 1

Lesson 3-7

Pre-

Act

ivit

yH

ow c

an p

erce

nts

des

crib

e gr

owth

ove

r ti

me?

Rea

d th

e in

trod

uct

ion

to

Les

son

3-7

at

the

top

of p

age

160

in y

our

text

book

.

•H

ow m

any

area

cod

es w

ere

in u

se i

n 1

947?

84 a

rea

cod

es•

How

man

y m

ore

area

cod

es w

ere

in u

se i

n 1

999?

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area

co

des

Rea

din

g t

he

Less

on

1.If

you

use

(or

igin

al a

mou

nt)

— (

new

am

oun

t) t

o fi

nd

the

chan

ge f

or a

per

cen

t of

ch

ange

pr

oble

m,t

hen

th

e pr

oble

m i

nvo

lves

a p

erce

nt

of

(in

crea

se/d

ecre

ase)

.

2.If

you

use

(n

ew a

mou

nt)

— (

orig

inal

am

oun

t) t

o fi

nd

the

chan

ge f

or a

per

cen

t of

ch

ange

pr

oble

m,t

hen

th

e pr

oble

m i

nvo

lves

a p

erce

nt

of

(in

crea

se/d

ecre

ase)

.

Com

ple

te t

he

char

t.

Ori

gin

alN

ew

Per

cen

t In

crea

se o

r A

mo

un

tA

mo

un

tP

erce

nt

Pro

po

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nP

erce

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Dec

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e?

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13�

incr

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7�

dec

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6.50

58�

incr

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fin

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disc

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do y

ou a

dd t

o or

su

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ct f

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th

e or

igin

al p

rice

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btr

act

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pin

g Y

ou

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emb

er

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you

rem

embe

r on

ly t

wo

thin

gs a

bou

t th

e ra

tio

use

d fo

r fi

ndi

ng

perc

ent

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han

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hat

shou

ld t

hey

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btr

act

the

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th

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lenc

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cGra

w-H

ill17

8G

lenc

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lgeb

ra 1

Usi

ng

Per

cen

tU

se w

hat

you

hav

e le

arn

ed a

bou

t p

erce

nt

to s

olve

eac

h p

rob

lem

.

A T

V m

ovie

had

a “

rati

ng”

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d a

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shar

e.”

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e ra

tin

g is

th

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tage

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hou

seh

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th

at w

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o th

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how

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wit

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turn

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turn

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um

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um

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was

air

ed.

An

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eac

h q

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tion

.

1.D

urin

g th

at s

ame

wee

k,a

spor

ts b

road

cast

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a r

atin

g of

22.

1 an

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43 s

hare

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how

tha

t th

e pe

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t of

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hou

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as a

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ind

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how

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5.F

ind

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du

rin

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wat

ched

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rial

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gram

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tory

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e la

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loca

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sta

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mer

cial

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e fo

r th

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hat

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ld it

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ve t

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last

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____

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____

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____

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AT

E__

____

____

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ER

IOD

____

_

3-7

3-7

1 �

�r �

s�

r�



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

So

lvin

g E

qu

atio

ns

and

Fo

rmu

las

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

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ER

IOD

____

_

3-8

3-8

©G

lenc

oe/M

cGra

w-H

ill17

9G

lenc

oe A

lgeb

ra 1

Lesson 3-8

Solv

e fo

r V

aria

ble

sS

omet

imes

you

may

wan

t to

sol

ve a

n eq

uati

on s

uch

as V

��w

hfo

ron

e of

its

var

iabl

es.F

or e

xam

ple,

if y

ou k

now

th

e va

lues

of

V,w

,an

d h

,th

en t

he

equ

atio

n

��

is m

ore

use

ful

for

fin

din

g th

e va

lue

of �

.If

an e

quat

ion

th

at c

onta

ins

mor

e th

an o

ne

vari

able

is

to b

e so

lved

for

a s

peci

fic

vari

able

,use

th

e pr

oper

ties

of

equ

alit

y to

iso

late

th

esp

ecif

ied

vari

able

on

on

e si

de o

f th

e eq

uat

ion

.

V � wh

Sol

ve 2

x�

4y�

8 fo

r y.

2x�

4y�

82x

�4y

�2x

�8

�2x

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�8

�2x

�

y�

or

Th

e va

lue

of y

is

.2x

�8

�4

2x�

8�

48

�2x

��

4

8 �

2x�

�4

�4y

� �4

Sol

ve 3

m�

n�

km

�8

for

m.

3m�

n�

km�

83m

�n

�km

�km

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km�

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km�

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�n

m(3

�k)

��

8 �

n

�

m�

,or

Th

e va

lue

of m

is

.Sin

ce d

ivis

ion

by

0 is

un

defi

ned

,3 �

k�

0,or

k�

3.

n�

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�k

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�k

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�n

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m(3

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��

3 �

k

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ple1

Exam

ple1

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ple2

Exam

ple2

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cises

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cises

Sol

ve e

ach

eq

uat

ion

or

form

ula

for

th

e va

riab

le s

pec

ifie

d.

1.ax

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for

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f) �

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for

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for

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x(1

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for

x

c�

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�rt

for

r12

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for

h

x�

r�

,t

0h

�,a

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b

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) fo

r F

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for

w15

.A�

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r �

F�

C�

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��

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A � wP

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9 � 5

5 � 9

2A� a

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d � ty

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z�

4

h(a

�b)

�� 2z

� 1 �

yc

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t � 4

m�

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9 �

z�

x

y�

1�

15c

�b

�a

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lenc

oe/M

cGra

w-H

ill18

0G

lenc

oe A

lgeb

ra 1

Use

Fo

rmu

las

Man

y re

al-w

orld

pro

blem

s re

quir

e th

e u

se o

f fo

rmu

las.

Som

etim

es s

olvi

ng

a fo

rmu

la f

or a

spe

cifi

ed v

aria

ble

wil

l h

elp

solv

e th

e pr

oble

m.

Th

e fo

rmu

la C

��

dre

pre

sen

ts t

he

circ

um

fere

nce

of

a ci

rcle

,or

the

dis

tan

ce a

rou

nd

th

e ci

rcle

,wh

ere

dis

th

e d

iam

eter

.If

an a

irp

lan

e co

uld

fly

aro

un

dE

arth

at

the

equ

ator

wit

hou

t st

opp

ing,

it w

ould

hav

e tr

avel

ed a

bou

t 24

,900

mil

es.

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d t

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dia

met

er o

f E

arth

.

C�

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en f

orm

ula

d�

Sol

ve f

or d

.

d�

Use

��

3.14

.

d�

7930

Sim

plify

.

Th

e di

amet

er o

f E

arth

is

abou

t 79

30 m

iles

.

1.G

EOM

ETRY

Th

e vo

lum

e of

a c

ylin

der

Vis

giv

en b

y th

e fo

rmu

la V

��

r2h

,wh

ere

ris

the

radi

us

and

his

th

e h

eigh

t.

a.S

olve

th

e fo

rmu

la f

or h

.h

�

b.

Fin

d th

e h

eigh

t of

a c

ylin

der

wit

h v

olu

me

2500

�fe

et a

nd

radi

us

10 f

eet.

25 f

t

2.W

ATE

R P

RES

SUR

ET

he

wat

er p

ress

ure

on

a s

ubm

erge

d ob

ject

is

give

n b

y P

�64

d,

whe

re P

is t

he p

ress

ure

in p

ound

s pe

r sq

uare

foo

t,an

d d

is t

he d

epth

of

the

obje

ct i

n fe

et.

a.S

olve

th

e fo

rmu

la f

or d

.d

�

b.

Fin

d th

e de

pth

of a

sub

mer

ged

obje

ct if

the

pre

ssur

e is

672

pou

nds

per

squa

re f

oot.

10.5

ft

3.G

RA

PHS

Th

e eq

uat

ion

of

a li

ne

con

tain

ing

the

poin

ts (

a,0)

an

d (0

,b)

is g

iven

by

the

form

ula

�

�1.

a.S

olve

th

e eq

uat

ion

for

y.

y�

b�1

��

b.

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ppos

e th

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ne

con

tain

s th

e po

ints

(4,

0),a

nd

(0,�

2).I

f x

�3,

fin

d y.

�

4.G

EOM

ETRY

Th

e su

rfac

e ar

ea o

f a

rect

angu

lar

soli

d is

giv

en b

y th

e fo

rmu

la

S�

2�w

�2�

h�

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,wh

ere

��

len

gth

,w�

wid

th,a

nd

h�

hei

ght.

a.S

olve

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e fo

rmu

la f

or h

.h

�

b.

Th

e su

rfac

e ar

ea o

f a

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lar

soli

d w

ith

len

gth

6 c

enti

met

ers

and

wid

th

3 ce

nti

met

ers

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2 sq

uar

e ce

nti

met

ers.

Fin

d th

e h

eigh

t.2

cm

S�

2�w

��

2��

2w

1 � 2

x � a

y � bx � a

P � 64V � �r2

24,9

00�

3.14

C � �

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

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)

So

lvin

g E

qu

atio

ns

and

Fo

rmu

las

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-8

3-8

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

So

lvin

g E

qu

atio

ns

and

Fo

rmu

las

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

3-8

3-8

©G

lenc

oe/M

cGra

w-H

ill18

1G

lenc

oe A

lgeb

ra 1

Lesson 3-8

Sol

ve e

ach

eq

uat

ion

or

form

ula

for

th

e va

riab

le s

pec

ifie

d.

1.7t

�x,

for

tt

�2.

e�

wp,

for

pp

�

3.q

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�r,

for

rr

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4m�

n�

m,f

or m

m�

5.7a

�b

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r a

a�

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�5c

�d

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,for

cc

�

7.x

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for

yy

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m �

3n�

1,fo

r n

n�

9.7f

�g

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for

ff

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.ax

�c

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for

xx

�

11.r

t�

2n�

y,fo

r t

t�

12.b

c�

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or c

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or n

n�

14.8

c�

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5p,f

or c

c�

15.

�d

,for

xx

�c

�2d

16.

�d

,for

cc

�x

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17.

�q,

for

pp

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18.

�a,

for

bb

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�4z

Wri

te a

n e

qu

atio

n a

nd

sol

ve f

or t

he

vari

able

sp

ecif

ied

.

19.F

ive

mor

e th

an a

nu

mbe

r g

is s

ix l

ess

than

tw

ice

a n

um

ber

h.S

olve

for

g.

g �

5 �

2h�

6;g

�2h

�11

20.O

ne

fou

rth

of

a n

um

ber

qis

th

ree

mor

e th

an t

hre

e ti

mes

a n

um

ber

w.S

olve

for

q.

q�

3w�

3;q

�12

w�

12

21.E

igh

t le

ss t

han

a n

um

ber

sis

th

ree

mor

e th

an f

our

tim

es a

nu

mbe

r t.

Sol

ve f

or s

.

s�

8 �

4t�

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1 � 4

b�

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x�

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89v

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b2n

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b�

c�

a5

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1 �

m�

3x

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d � 7b � 8

n � 3q � 2

e � wx � 7

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lenc

oe/M

cGra

w-H

ill18

2G

lenc

oe A

lgeb

ra 1

Sol

ve e

ach

eq

uat

ion

or

form

ula

for

th

e va

riab

le s

pec

ifie

d.

1.d

�rt

,for

rr

�2.

6w�

y�

2z,f

or w

w�

3.m

x�

4y�

3c,f

or x

x�

4.9s

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��

4u,f

or s

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5.ab

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,for

bb

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2p�

kx�

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r x

x�

7.m

�a

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�c,

for

mm

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�g

�d

,for

hh

�(d

�g

)

9.y

�v

�s,

for

yy

�(s

�v)

10.

a�

q�

k,fo

r a

a�

(k�

q)

11.

�h

,for

xx

�12

.�

c,fo

r b

b�

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w�

y�

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r w

w�

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y�

5 �

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or �

��

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te a

n e

qu

atio

n a

nd

sol

ve f

or t

he

vari

able

sp

ecif

ied

.

15.T

hre

e ti

mes

a n

um

ber

spl

us

4 ti

mes

a n

um

ber

yis

1 m

ore

than

6 t

imes

th

e n

um

ber

s.S

olve

for

s.

3s�

4y�

6s�

1;s

�

16.F

ive

tim

es a

nu

mbe

r k

min

us

9 is

tw

o th

irds

of

a n

um

ber

j.S

olve

for

j.

5k�

9 �

j;j�

(5k

�9)

ELEC

TRIC

ITY

For

Exe

rcis

es 1

7 an

d 1

8,u

se t

he

foll

owin

g in

form

atio

n.

Th

e fo

rmu

la f

or O

hm

’s L

aw i

s E

�IR

,wh

ere

Ere

pres

ents

vol

tage

mea

sure

d in

vol

ts,

Ire

pres

ents

cu

rren

t m

easu

red

in a

mpe

res,

and

Rre

pres

ents

res

ista

nce

mea

sure

d in

oh

ms.

17.S

olve

th

e fo

rmu

la f

or R

.R

�

18.S

upp

ose

a cu

rren

t of

0.2

5 am

pere

flo

ws

thro

ugh

a r

esis

tor

con

nec

ted

to a

12-

volt

bat

tery

.W

hat

is

the

resi

stan

ce i

n t

he

circ

uit

?48

oh

ms

MO

TIO

NF

or E

xerc

ises

19

and

20,

use

th

e fo

llow

ing

info

rmat

ion

.

In u

nif

orm

cir

cula

r m

otio

n,t

he

spee

d v

of a

poi

nt

on t

he

edge

of

a sp

inn

ing

disk

is

v�

r,

wh

ere

ris

th

e ra

diu

s of

th

e di

sk a

nd

Tis

th

e ti

me

it t

akes

th

e po

int

to t

rave

l on

ce a

rou

nd

the

circ

le.

19.S

olve

th

e fo

rmu

la f

or r

.r

�

20.S

upp

ose

a m

erry

-go-

rou

nd

is s

pin

nin

g on

ce e

very

3 s

econ

ds.I

f a

poin

t on

th

e ou

tsid

eed

ge h

as a

spe

ed o

f 12

.56

feet

per

sec

ond,

wh

at i

s th

e ra

diu

s of

th

e m

erry

-go-

rou

nd?

(U

se 3

.14

for

�.)

6 ft

Tv

� 2�

2� � T

E � I

3 � 22 � 3

4y�

1�

3

y�

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22

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2c�

4�

33b

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5h�

9�

rrx

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4 � 33 � 4

3 � 22 � 3

5 � 22 � 5

3 � 22 � 3

2p�

q�

k2d

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�4u

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�� 9

3c�

4y�

m

2z�

y�

6d � t

Pra

ctic

e (

Ave

rag

e)

So

lvin

g E

qu

atio

ns

and

Fo

rmu

las

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-8

3-8



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csS

olv

ing

Eq

uat

ion

s an

d F

orm

ula

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-8

3-8

©G

lenc

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cGra

w-H

ill18

3G

lenc

oe A

lgeb

ra 1

Lesson 3-8

Pre-

Act

ivit

yH

ow a

re e

qu

atio

ns

use

d t

o d

esig

n r

olle

r co

aste

rs?

Rea

d th

e in

trod

uct

ion

to

Les

son

3-8

at

the

top

of p

age

166

in y

our

text

book

.

Th

e eq

uat

ion

g(1

95 �

h)

�v2

con

tain

s se

vera

l va

riab

les.

Wh

at

nu

mbe

r va

lues

do

you

kn

ow f

or t

hes

e va

riab

les

in t

his

sit

uat

ion

?

32 f

or

gan

d 4

9 fo

rv

Rea

din

g t

he

Less

on

1.S

upp

ose

you

hav

e an

equ

atio

n w

ith

sev

eral

var

iabl

es.Y

ou w

ant

to s

olve

for

a p

arti

cula

rva

riab

le.H

ow d

oes

the

proc

edu

re c

ompa

re w

ith

th

at f

or s

olvi

ng

an e

quat

ion

wit

h ju

ston

e va

riab

le?

How

doe

s th

e so

luti

on c

ompa

re w

ith

th

e so

luti

on f

or a

n e

quat

ion

wit

h o

ne

vari

able

?

Sam

ple

an

swer

: T

he

pro

ced

ure

is b

asic

ally

th

e sa

me.

Yo

u u

se p

rop

erti

eso

f o

per

atio

ns

and

eq

ual

ity

to is

ola

te t

he

vari

able

in w

hic

h y

ou

are

inte

rest

ed. T

he

solu

tio

n w

ill p

rob

ably

co

nta

in v

aria

ble

s in

stea

d o

f ju

st a

nu

mb

er.

2.D

escr

ibe

wh

at d

imen

sion

al a

nal

ysis

in

volv

es.

Sam

ple

an

swer

: Yo

u u

se t

he

un

its

alo

ng

wit

h n

um

ber

val

ues

as

you

do

calc

ula

tio

ns.

Yo

u t

reat

th

e u

nit

s p

rett

y m

uch

th

e sa

me

way

yo

u w

ou

ldva

riab

les.

Fo

r ex

amp

le, y

ou

can

div

ide

them

an

d u

se e

xpo

nen

ts w

ithth

em.

3.W

hat

do

you

hav

e to

be

care

ful

abou

t w

hen

you

use

var

iabl

es i

n d

enom

inat

ors

offr

acti

ons?

You

hav

e to

be

sure

th

at y

ou

do

no

t u

se v

alu

es t

hat

wo

uld

mak

e th

ed

eno

min

ato

r 0.

Hel

pin

g Y

ou

Rem

emb

er

4.W

hen

you

giv

e th

e di

men

sion

s of

a r

ecta

ngl

e,yo

u h

ave

to t

ell

how

man

y u

nit

s lo

ng

it i

san

d h

ow m

any

un

its

wid

e it

is.

How

can

th

is h

elp

you

rem

embe

r w

hat

dim

ensi

onal

anal

ysis

in

volv

es.

Sam

ple

an

swer

: K

eep

th

e w

ord

s d

imen

sio

nan

d u

nit

in m

ind

. In

dim

ensi

on

al a

nal

ysis

, yo

u in

clu

de

un

its

for

dim

ensi

on

s in

cal

cula

tio

ns.

1 � 2

©G

lenc

oe/M

cGra

w-H

ill18

4G

lenc

oe A

lgeb

ra 1

Dr.

Ber

nar

do

Ho

uss

ay

Eve

n t

hou

gh r

esea

rch

ers

hav

e be

en s

tudy

ing

the

dise

ase

dia

bete

sm

elli

tus

for

hu

ndr

eds

of y

ears

,sci

enti

sts

hav

e on

ly r

ecen

tly

disc

over

edth

e ca

use

of

the

dise

ase

and

deve

lope

d m

eth

ods

for

redu

cin

g it

sse

veri

ty.D

r.B

ern

ardo

Hou

ssay

,an

Arg

enti

ne

phys

iolo

gist

,was

on

e of

the

pion

eers

of

this

mor

e m

oder

n r

esea

rch

.He

stu

died

th

e re

lati

onsh

ipbe

twee

n d

iabe

tes

and

the

pitu

itar

y gl

and,

and

in 1

947

beca

me

the

firs

tL

atin

Am

eric

an t

o w

in t

he

Nob

el P

rize

in

Med

icin

e an

d P

hys

iolo

gy.

Tho

ugh

ther

e is

no

cure

for

dia

bete

s,sp

ecif

ic d

iets

and

exe

rcis

e ca

n he

lppe

ople

con

trol

the

dis

ease

.The

Am

eric

an D

iabe

tes

Ass

ocia

tion

(A

DA

)ha

s he

lped

est

abli

sh f

lexi

ble

diet

ary

guid

elin

es f

or c

onsu

mer

s to

fol

low

.T

hese

gui

deli

nes

incl

ude

som

e of

the

fol

low

ing

gene

ral

nutr

itio

n ru

les.

•Fa

t in

take

sh

ould

be

equ

al t

o or

les

s th

an 3

0% o

f da

ily

calo

ries

.

•S

atu

rate

d fa

t in

take

sh

ould

be

equ

al t

o or

les

s th

an 1

0% o

f da

ily

calo

ries

.

•P

rote

in s

hou

ld b

e li

mit

ed t

o 10

% t

o 20

% o

f da

ily

calo

ries

.Per

son

ssh

owin

g th

e in

itia

l si

gns

of d

iabe

tes-

indu

ced

kidn

ey d

isea

se s

hou

ldli

mit

pro

tein

to

10%

of

dail

y ca

lori

es.

•C

hol

este

rol

inta

ke s

hou

ld b

e 30

0 m

illi

gram

s or

les

s da

ily.

Ref

er t

o th

e in

form

atio

n a

bov

e fo

r E

xerc

ises

1–4

.

1.R

ober

t co

nsu

med

210

0 ca

lori

es o

n T

ues

day.

His

fat

in

take

tot

aled

70 g

ram

s,an

d of

th

at 7

0 gr

ams,

14 w

ere

satu

rate

d.

a.W

hat

per

cen

tage

of

his

cal

orie

con

sum

ptio

n w

as f

at,a

nd

wh

atpe

rcen

tage

of

that

fat

was

sat

ura

ted?

(T

o fi

nd

the

perc

enta

ge o

fca

lori

es f

rom

fat

,mu

ltip

ly t

he

nu

mbe

r of

fat

gra

ms

by 9

bef

ore

divi

din

g by

th

e n

um

ber

of c

alor

ies.

) 30

%;

20%

b.

Did

Rob

ert

stay

wit

hin

th

e re

com

men

ded

allo

wan

ce o

f fa

ts?

yes

2.A

nn

a's

chol

este

rol

inta

ke w

as 3

30 m

illi

gram

s on

Su

nda

y.B

y w

hat

perc

enta

ge d

oes

she

nee

d to

red

uce

her

ch

oles

tero

l co

nsu

mpt

ion

to

rem

ain

wit

hin

th

e gu

idel

ines

? 10

%

3.W

hat

nu

mbe

r of

fat

gra

ms

is 3

0% o

f 24

0 ca

lori

es?

8

4.S

har

on f

ollo

ws

a di

et t

hat

pro

vide

s ab

out

50 g

ram

s of

pro

tein

eac

hda

y.S

har

on's

doc

tor

has

just

tol

d h

er t

o re

duce

her

dai

ly p

rote

inin

take

by

30%

.Abo

ut

how

mu

ch p

rote

in w

ill

be i

n h

er r

edu

ced

prot

ein

die

t?35

gra

ms

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-8

3-8



Stu

dy G

uid

e a

nd I

nte

rven

tion

Wei

gh

ted

Ave

rag

es

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-9

3-9

©G

lenc

oe/M

cGra

w-H

ill18

5G

lenc

oe A

lgeb

ra 1

Lesson 3-9

Mix

ture

Pro

ble

ms

Wei

gh

ted

Ave

rag

eT

he w

eigh

ted

aver

age

Mof

a s

et o

f da

ta is

the

sum

of

the

prod

uct

of e

ach

num

ber

in

the

set

and

its w

eigh

t di

vide

d by

the

sum

of

all t

he w

eigh

ts.

Mix

ture

Pro

ble

ms

are

prob

lem

s w

her

e tw

o or

mor

e pa

rts

are

com

bin

ed i

nto

a w

hol

e.T

hey

invo

lve

wei

ghte

d av

erag

es.I

n a

mix

ture

pro

blem

,th

e w

eigh

t is

usu

ally

a p

rice

or

a pe

rcen

tof

som

eth

ing.

Del

ecta

ble

Coo

kie

Com

pan

y se

lls

choc

olat

e ch

ip c

ook

ies

for

$6.9

5p

er p

oun

d a

nd

wh

ite

choc

olat

e co

okie

s fo

r $5

.95

per

pou

nd

.How

man

y p

oun

ds

ofch

ocol

ate

chip

coo

kie

s sh

ould

be

mix

ed w

ith

4 p

oun

ds

of w

hit

e ch

ocol

ate

cook

ies

to o

bta

in a

mix

ture

th

at s

ells

for

$6.

75 p

er p

oun

d.

Let

w�

the

nu

mbe

r of

pou

nds

of

choc

olat

e ch

ip c

ooki

es

Nu

mb

er o

f P

ou

nd

sP

rice

per

Po

un

dTo

tal P

rice

Ch

oco

late

Ch

ipw

6.95

6.95

w

Wh

ite

Ch

oco

late

45.

954(

5.95

)

Mix

ture

w�

46.

756.

75(w

�4)

Equ

atio

n:6

.95w

�4(

5.95

) �

6.75

(w�

4)S

olve

th

e eq

uat

ion

.6.

95w

�4(

5.95

)�

6.75

(w�

4)O

rigin

al e

quat

ion

6.95

w�

23.8

0�

6.75

w�

27S

impl

ify.

6.95

w�

23.8

0 �

6.75

w�

6.75

w�

27 �

6.75

wS

ubtr

act

6.75

wfr

om e

ach

side

.

0.2w

�23

.80

�27

Sim

plify

.

0.2w

�23

.80

�23

.80

�27

�23

.80

Sub

trac

t 23

.80

from

eac

h si

de.

0.2w

�3.

2S

impl

ify.

w�

16S

impl

ify.

16 p

ound

s of

cho

cola

te c

hip

cook

ies

shou

ld b

e m

ixed

wit

h 4

poun

ds o

f w

hite

cho

cola

te c

ooki

es.

1.SO

LUTI

ON

SH

ow m

any

gram

s of

su

gar

mu

st b

e ad

ded

to 6

0 gr

ams

of a

sol

uti

on t

hat

is

32%

su

gar

to o

btai

n a

sol

uti

on t

hat

is

50%

su

gar?

21.6

g

2.N

UTS

Th

e Q

uik

Mar

t h

as t

wo

kin

ds o

f n

uts

.Pec

ans

sell

for

$1.

55 p

er p

oun

d an

dw

aln

uts

sel

l fo

r $1

.95

per

pou

nd.

How

man

y po

un

ds o

f w

aln

uts

mu

st b

e ad

ded

to 1

5po

un

ds o

f pe

can

s to

mak

e a

mix

ture

th

at s

ells

for

$1.

75 p

er p

oun

d?15

lb

3.IN

VES

TMEN

TSA

lice

Gle

ason

in

vest

ed a

por

tion

of

$32,

000

at 9

% i

nte

rest

an

d th

eba

lan

ce a

t 11

% i

nte

rest

.How

mu

ch d

id s

he

inve

st a

t ea

ch r

ate

if h

er t

otal

in

com

e fr

ombo

th i

nve

stm

ents

was

$3,

200.

$16,

000

at 9

% a

nd

$16

,000

at

11%

4.M

ILK

Wh

ole

mil

k is

4%

bu

tter

fat.

How

mu

ch s

kim

mil

k w

ith

0%

bu

tter

fat

shou

ld b

ead

ded

to 3

2 ou

nce

s of

wh

ole

mil

k to

obt

ain

a m

ixtu

re t

hat

is

2.5%

bu

tter

fat?

19.2

oz

Exam

ple

Exam

ple

Exer

cises

Exer

cises

©G

lenc

oe/M

cGra

w-H

ill18

6G

lenc

oe A

lgeb

ra 1

Un

ifo

rm M

oti

on

Pro

ble

ms

Mot

ion

pro

blem

s ar

e an

oth

er a

ppli

cati

on o

f w

eigh

ted

aver

ages

.Un

ifor

m m

otio

n p

rob

lem

sar

e pr

oble

ms

wh

ere

an o

bjec

t m

oves

at

a ce

rtai

nsp

eed,

or r

ate.

Use

th

e fo

rmu

la d

�rt

to s

olve

th

ese

prob

lem

s,w

her

e d

is t

he

dist

ance

,ris

the

rate

,an

d t

is t

he

tim

e.

Bil

l G

uti

erre

z d

rove

at

a sp

eed

of

65 m

iles

per

hou

r on

an

exp

ress

way

for

2 h

ours

.He

then

dro

ve f

or 1

.5 h

ours

at

a sp

eed

of

45 m

iles

per

hou

r on

a s

tate

hig

hw

ay.W

hat

was

his

ave

rage

sp

eed

?

M�

Def

initi

on o

f w

eigh

ted

aver

age

�56

.4S

impl

ify.

Bil

l dr

ove

at a

n a

vera

ge s

peed

of

abou

t 56

.4 m

iles

per

hou

r.

1.TR

AV

ELM

r.A

nde

rs a

nd

Ms.

Ric

h e

ach

dro

ve h

ome

from

a b

usi

nes

s m

eeti

ng.

Mr.

An

ders

trav

eled

eas

t at

100

kil

omet

ers

per

hou

r an

d M

s.R

ich

tra

vele

d w

est

at 8

0 ki

lom

eter

s pe

rh

ours

.In

how

man

y h

ours

wer

e th

ey 1

00 k

ilom

eter

s ap

art.

h

2.A

IRPL

AN

ESA

n a

irpl

ane

flie

s 75

0 m

iles

du

e w

est

in 1

hou

rs a

nd

750

mil

es d

ue

sou

th

in 2

hou

rs.W

hat

is

the

aver

age

spee

d of

th

e ai

rpla

ne?

abo

ut

429

mp

h

3.TR

AC

KS

prin

ter

A r

un

s 10

0 m

eter

s in

15

seco

nds

,wh

ile

spri

nte

r B

sta

rts

1.5

seco

nds

late

r an

d ru

ns

100

met

ers

in 1

4 se

con

ds.I

f ea

ch o

f th

em r

un

s at

a c

onst

ant

rate

,wh

o is

furt

her

in

10

seco

nds

aft

er t

he

star

t of

th

e ra

ce?

Exp

lain

.

Sp

rin

ter

A;

sin

ce s

pri

nte

r A

ru

ns

100

m in

15

s,th

is s

pri

nte

r ru

ns

at a

rate

of

m/s

.In

10

seco

nd

s,sp

rin

ter

A w

ill h

ave

run

(1

0) �

66.7

m.

Sp

rin

ter

B’s

rat

e is

.I

n 1

0 se

con

ds,

wit

h t

he

del

ayed

sta

rt,s

pri

nte

r B

has

ru

n

(10

�1.

5) �

60.7

m.

4.TR

AIN

SA

n e

xpre

ss t

rain

tra

vels

90

kilo

met

ers

per

hou

r fr

om S

mal

lvil

le t

o M

egat

own

.A

loc

al t

rain

tak

es 2

.5 h

ours

lon

ger

to t

rave

l th

e sa

me

dist

ance

at

50 k

ilom

eter

s pe

rh

our.

How

far

apa

rt a

re S

mal

lvil

le a

nd

Meg

atow

n?

281.

25 k

m

5.C

YC

LIN

GT

wo

cycl

ists

beg

in t

rave

lin

g in

th

e sa

me

dire

ctio

n o

n t

he

sam

e bi

ke p

ath

.On

etr

avel

s at

15

mil

es p

er h

our,

and

the

oth

er t

rave

ls a

t 12

mil

es p

er h

our.

Wh

en w

ill

the

cycl

ists

be

10 m

iles

apa

rt?

3h

6.TR

AIN

ST

wo

trai

ns

leav

e C

hic

ago,

one

trav

elin

g ea

st a

t 30

mil

es p

er h

our

and

one

trav

elin

g w

est

at 4

0 m

iles

per

hou

r.W

hen

wil

l th

e tr

ain

s be

210

mil

es a

part

?3

h

1 � 3

100

� 14

100

� 14

100

� 1510

0� 15

1 � 2

5 � 9

65

2 �

45

1.5

��

2 �

1.5

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Wei

gh

ted

Ave

rag

es

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-9

3-9

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Skil

ls P

ract

ice

Wei

gh

ted

Ave

rag

es

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

3-9

3-9

©G

lenc

oe/M

cGra

w-H

ill18

7G

lenc

oe A

lgeb

ra 1

Lesson 3-9

SEA

SON

ING

For

Exe

rcis

es 1

–4,u

se t

he

foll

owin

g in

form

atio

n.

A h

ealt

h f

ood

stor

e se

lls

seas

onin

g bl

ends

in

bu

lk.O

ne

blen

d co

nta

ins

20%

bas

il.S

hei

law

ants

to

add

pure

bas

il t

o so

me

20%

ble

nd

to m

ake

16 o

un

ces

of h

er o

wn

30%

ble

nd.

Let

bre

pres

ent

the

amou

nt

of b

asil

Sh

eila

sh

ould

add

to

the

20%

ble

nd.

1.C

ompl

ete

the

tabl

e re

pres

enti

ng

the

prob

lem

.

Ou

nce

sA

mo

un

t o

f B

asil

20%

Bas

il B

len

d16

�b

0.20

(16

�b

)

100%

Bas

ilb

1.00

b

30%

Bas

il B

len

d16

0.30

(16)

2.W

rite

an

equ

atio

n t

o re

pres

ent

the

prob

lem

.0.

20(1

6 �

b)

�1.

00b

�0.

30(1

6)

3.H

ow m

any

oun

ces

of b

asil

sh

ould

Sh

eila

use

to

mak

e th

e 30

% b

len

d?2

oz

4.H

ow m

any

oun

ces

of t

he

20%

ble

nd

shou

ld s

he

use

?14

oz

HIK

ING

For

Exe

rcis

es 5

–7,u

se t

he

foll

owin

g in

form

atio

n.

At

7:00

A.M

.,tw

o gr

oups

of

hik

ers

begi

n 2

1 m

iles

apa

rt a

nd

hea

d to

war

d ea

ch o

ther

.Th

e fi

rst

grou

p,h

ikin

g at

an

ave

rage

rat

e of

1.5

mil

es p

er h

our,

carr

ies

ten

ts,s

leep

ing

bags

,an

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wo

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t 50

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how

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3-9

3-9



Readin

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Math

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vera

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3-9

3-9

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Lesson 3-9

Pre-

Act

ivit

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ow a

re s

core

s ca

lcu

late

d i

n a

fig

ure

sk

atin

g co

mp

etit

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?

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d th

e in

trod

uct

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to

Les

son

3-9

at

the

top

of p

age

171

in y

our

text

book

.

Wh

y is

th

e su

m o

f Il

ia K

uli

k’s

scor

es d

ivid

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y 3?

Her

fir

st s

core

is c

ou

nte

d o

nce

an

d h

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eco

nd

sco

re is

cou

nte

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wic

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din

g t

he

Less

on

1.R

ead

the

defi

nit

ion

of

wei

ghte

d a

vera

geon

pag

e 17

1 of

you

r te

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hat

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byth

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t of

a n

um

ber

in a

set

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the

nu

mb

er o

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mes

th

e n

um

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urs

in t

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dat

a

2.L

inda

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re 9

0,85

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75,8

5,an

d 90

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th

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dete

rmin

ate

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atio

ns.

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in

dete

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ate

equ

atio

n h

as m

ore

than

on

e va

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anu

nli

mit

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n e

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ple

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en t

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you

are

ask

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o fi

nd

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s th

at m

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inte

gers

,th

e eq

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is

call

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ind

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100

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3-9

3-9



Chapter 3 Assessment Answer Key Form 1 Form 2APage 191 Page 192 Page 193

An

swer

s

(continued on the next page)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. B

C

D

C

A

D

B

C

A

B

45

A

B

D

B

C

C

D

A

C

B

D

A

B

B

A

C

D

B

D

D


11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 21

C

A

A

B

D

B

A

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D

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B

A

C

B

D

A

B

C

C

A

3.6 L

C

B

A

D

B

C

B

C

A

B

Chapter 3 Assessment Answer Key Form 2A (continued) Form 2BPage 194 Page 195 Page 196


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 8

h � ��Vr 2�; 10.5 in.

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3 L

$12.84

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13

all numbers

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yes

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5n � 12 � �3; �3

n � 3.5 � 12.7;16.2

Three times the sumof x and y equals two

times y minus x.

36 � x � 3(4 � x)

6

45

14�25

�

�186

5

�5

�35

�

�9

Chapter 3 Assessment Answer Key Form 2CPage 197 Page 198

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: $9.60

h � ��Vr 2�; 18.67 in.

4 h

7.5 lb of nuts,2.5 lb of dried fruit

$13.50

increase; 25%

r � s(4v � t)

11

no solution

3

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no

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6n � 15 � 9; �1

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Three divided by y minusfive equals x times thesum of y and 7.

18 � n � 7(n � 3)

7

50

7�57

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7

7

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4

Chapter 3 Assessment Answer Key Form 2DPage 199 Page 200


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 12 mi

3 ft/s

510 mph, 540 mph

$7000

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x � �rs

4� t�

x � �r �

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(x � 2)10 � 8x � 36; 8

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126

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Chapter 3 Assessment Answer Key Form 3Page 201 Page 202

An

swer

sA

nsw

ers

Five times the sum oftwo times x and threetimes y equals thesquare of y minus twotimes the cube of x.


Chapter 3 Assessment Answer KeyPage 203, Open-Ended Assessment

Scoring Rubric

Score General Description Specific Criteria

• Shows thorough understanding of the concepts oftranslating between verbal sentences and equations,solving equations, percents of increase and decrease,uniform motion problems, and proportions.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Goes beyond requirements of some or all problems.

• Shows an understanding of the concepts of translatingbetween verbal sentences and equations, solvingequations, percents of increase and decrease, uniformmotion problems, and proportions.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts oftranslating between verbal sentences and equations,solving equations, percents of increase and decrease,uniform motion problems, and proportions.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of most of the concepts oftranslating between verbal sentences and equations,solving equations, percents of increase and decrease,uniform motion problems, and proportions.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Does not satisfy requirements of problems.• No answer may be given.

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

4 SuperiorA correct solution that is supported by well-developed, accurateexplanations

Chapter 3 Assessment Answer Key Page 203, Open-Ended Assessment

Sample Answers


1a. The student should explain that thefirst phrase is a product of x and y andthen the addition of z, while the secondphrase is a product of x and thequantity y � z.

1b. Check that the student’s values for x,y, and z satisfy both xy � z andx(y � z). One example is x � 1, y � 2,and z � 3. Another example is x � 2,y � 3, and z � 0.

2a. �ry

m� s� � t � x

(Original equation)

�ry

m� s� � t � t � x � t

(Add t to each side.)

�ry

m� s� � x � t

(Simplify.)

m��rym� s�� m(x � t)

(Multiply each side by m.)ry � s � mx � mt

(Simplify.)ry � s � s � mx � mt � s

(Subtract s from each side.)ry � mx � mt � s

(Simplify.)

�rry� � �

mx �rmt � s�

(Divide each side by r.)

y � �mx �

rmt � s�

(Simplify.)The value of y is �mx �

rmt � s�.

2b. Division by 0 is undefined, so in theoriginal equation m � 0, and in thefinal equation r � 0.

3a. The student should conclude that a10% decrease followed by a 10%increase results in a net decrease of1%. Thus, the final cost would be 99%of the original price.

3b. Since multiplication is commutative,multiplying by 1.1 and then 0.9 wouldyield the same result as multiplying by0.9 and then 1.1. The student shouldconclude that a 10% increase followedby a 10% decrease yields the sameresult as a 10% decrease followed by a 10% increase.

4a. Since the two people walked for thesame amount of time and time can becalculated as distance divided by rate,the proportion

�

can be used to solve this problem.4b. The length of Tony’s walk can be

calculated directly from his rate of 3 miles per hour and his distance of 6 miles. Ivia walked 1 mile per hourfaster, so her rate is 4 miles per hour.The length of Ivia’s walk can be calculated directly from her rate of 4 miles per hour and distance of 6 miles. Thus, a proportion would notbe used to solve this problem.

5a. Sample answer: x � 2 � 10, x � 2 � 6,2x � 16, �2

x� � 4

5b. Sample answer: 2x � 1 � x � 95c. These two equations are equivalent.

The solution to both equations is 5.The student should recognize that thesolution to all equations in parts a andb is 8. Therefore neither of these twoequations could be equivalent to any of the equations created for parts aand b.

Ivia’s distance��Ivia’s rate

Tony’s distance��Tony’s rate

In addition to the scoring rubric found on page A34, the following sample answers may be used as guidance in evaluating open-ended assessment items.

An

swer

s


1. false; added to

2. true

3. true

4. false; more

5. false; true

6. false; division

7. true

8. true

9. false; percent ofdecrease

10. false; percent ofincrease

11. an equation statingthat two ratios areequal

12. an equation thatstates a rule for therelationshipbetween certainquantities

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lessons 3-4 and 3-5)

Page 205

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lessons 3-8 and 3-9)

Page 206

1.

2.

3.

4.

5.� � �

P �2

2w�; 14 m

2.4 mph

4 g

b � x � ac

x � �p �

nm

�

$75.60

$19.08

increase; 25%

decrease; 28%

99

27

15

no

no

yes

135

2

C

7

0

no solution

�5

�5�35

�

84

7

�40

40

�9

�9

�49

14

Two times b minus10 equals 4.

y2 � 12 � 5x

2n � 3(n � 9)

Chapter 3 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 3-1 through 3-3) Quiz (Lessons 3-6 and 3-7)

Page 204 Page 205 Page 206

The sum of y and the productof three and the square of xis five times x.


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

1.

2.

3. Sample answer:

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16. 7 L

m � n(q � p)

3

�3

7

31

85 � 9y � 7(4 � y)

1:3

115 120 125 130 135

� � � ��

��

��

�1.3

�13

�384

16.9

5u � 9v

22

Three times the sumof y and 5 equals theproduct of y and 7.

Four times nequals m timesthe difference offive and n.

$116.15

�2

all numbers

0

Part II

C

B

C

A

D

B

Part I

Chapter 3 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 207 Page 208

An

swer

s

y

xO


1.

2.

3.

4.

5.

6.

7.

8.

9.

10. 11.

12. 13.

14.

15.

16. DCBA

DCBA

DCBA

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

52

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

1 / 4

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

1 1 2/

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

3 2/

DCBA

HGFE

DCBA

DCBA

DCBA

HGFE

DCBA

HGFE

DCBA

Chapter 3 Assessment Answer KeyStandardized Test Practice

Page 209 Page 210


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30. 8 lb

v � t � sr

$3.91

3�27

�

all real numbers

�2

56

42

�12

�18

�3.6�5�, ��158�, �

7251�, �13�

irrational, real

Median; most of thedata clusters near the

median.

0 5 10 15

��

� � ��

� ��

��

5 : 1

�14

� or 25%

�4.7

��23

�

�47

�2�3 �1 0 1 2 4 5 6 7 83

40 peopleTime

Tem

per

atu

re (

F°)

H: a figure is a triangle;C: it is a polygon; If afigure is a triangle, thenit is a polygon.

23a � 6b

7r � 9t

7t2 � 3t

MultiplicativeInverse Property; �

16

�

{4}

71

5 � n3

Chapter 3 Assessment Answer Key Unit 1 TestPage 211 Page 212

An

swer

s

Documents

Chapter 3 Resource Masters - Morgan Park High School · 2009. 12. 2. · ©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 3 Resource Masters The Fast