Handout Solve the following applications. Draw a table or diagram when necessary

HandoutHandout

Solve the following Solve the following applications. Draw a table or applications. Draw a table or

diagram when necessary.diagram when necessary.

Solving Application Solving Application Problems.Problems.

Use ISSUEUse ISSUE I – IdentifyI – Identify S – SetupS – Setup S – SolveS – Solve U – UnderstandU – Understand E - ExplainE - Explain

1. The sum of two times a 1. The sum of two times a number and 7 is 35. What is number and 7 is 35. What is

the number?the number?

An equations is made up of two equal An equations is made up of two equal expressions. expressions.

The first step is to find the equal sign.The first step is to find the equal sign.

Where is the equal sign in this equation?Where is the equal sign in this equation?

Now, translate the left and right side of the Now, translate the left and right side of the equal sign.equal sign.



What does sum mean?What does sum mean?

What does two times a number mean?What does two times a number mean?

Is twice the number the same as two Is twice the number the same as two times the number?times the number?

Translate Translate “The sum of two times a number and “The sum of two times a number and 7”.7”.



2x + 72x + 7

Now, translate the right side of the Now, translate the right side of the equal sign.equal sign.

2x + 7 = 352x + 7 = 35



Solve the equationSolve the equation 2x + 7 = 35 2x + 7 = 35

2x + 7 +(-7) = 35 + ( -7)2x + 7 +(-7) = 35 + ( -7)

2x = 282x = 28

x = 14x = 14

Write the answer in a sentence.Write the answer in a sentence.

The number is 14.The number is 14.

2. 12 less than 5 times a 2. 12 less than 5 times a number is 78. What is the number is 78. What is the

number?number?

Solve the equationSolve the equation 5x - 12 = 78 5x - 12 = 78

5x - 12 + (12) = 78 + (12)5x - 12 + (12) = 78 + (12)

5x = 905x = 90

x = 18x = 18



(Try this one on your own.)

3. 3 times a number increased 3. 3 times a number increased by 8 is 62. What is the by 8 is 62. What is the

number?number?

Solve the equationSolve the equation 3x + 8 = 62 3x + 8 = 62

3x + 8 + (-8) = 62 + (-8)3x + 8 + (-8) = 62 + (-8)

3x = 543x = 54

x = 18x = 18




Click here to skip this one.

4. One number is 5 more than 4. One number is 5 more than another. If the sum of the another. If the sum of the numbers is 55, what are the numbers is 55, what are the numbers?numbers?

Identify the given Identify the given information.information.

Set up the equationSet up the equation11stst num. + 2 num. + 2ndnd num = sum num = sum

x + x + 5 = 55x + x + 5 = 55 Solve the equationSolve the equation 2x + 5 = 552x + 5 = 55 2x + 5 +(-5) = 55 +(-5)2x + 5 +(-5) = 55 +(-5) 2x = 502x = 50 x = 25x = 25

1st number

2nd number

Sum

x

x + 5

55

X = 25 is one number .What is the second number?

4. One number is 5 more than 4. One number is 5 more than another. If the sum of the another. If the sum of the numbers is 55, what are the numbers is 55, what are the numbers?numbers?

x + x + 5 = 55 x + x + 5 = 55

2x + 5 = 552x + 5 = 55

2x + 5 +(-5) = 55 +(-2x + 5 +(-5) = 55 +(-5)5)

2x = 502x = 50

x = 25x = 25

and and

x + 5 = 30x + 5 = 30

1st number

2nd number

Sum

x

x + 5

55

The numbers are 25 and 30.

5. One number is 3 times the 5. One number is 3 times the another. If the sum of the another. If the sum of the numbers is 64, what are the numbers is 64, what are the numbers?numbers?


Set up the equationSet up the equation11stst num. + 2 num. + 2ndnd num = num = sumsum

x + 3x = 64x + 3x = 64 Solve the equationSolve the equation

4x = 644x = 64

x = 16x = 16

1st number

2nd number

Sum

x

3x

64

X = 16 is one number .What is the second number?


The numbers are 16 and 48.

6. John earns $7 an hour less than 6. John earns $7 an hour less than Mary. Together they earn $33 per Mary. Together they earn $33 per hour. How much does each earn?hour. How much does each earn?


Set up the equationSet up the equation John + Mary = sumJohn + Mary = sum

x – 7 + x = 33x – 7 + x = 33 Solve the equationSolve the equation

2x – 7 = 332x – 7 = 33

x = 20x = 20

John

Mary

Sum

X – 7

X

33

Mary earns $20 per hour.How much does John earn?

(REVISED.)

John earns $13 per hour and Mary earns $20 per hour.

8. The length of a rectangle is 5 8. The length of a rectangle is 5 cm more than the width. The cm more than the width. The perimeter is 98 cm. Find the perimeter is 98 cm. Find the dimensions of the rectangle?dimensions of the rectangle?


Set up the equationSet up the equation 2L + 2W = P2L + 2W = P

2(x + 5) + 2(x) = 982(x + 5) + 2(x) = 98 Solve the equationSolve the equation

2x + 10 + 2x = 982x + 10 + 2x = 98

x = 22x = 22

Length

Width

Perimeter

X + 5

X

98

The width is 22 cm.What is the length?

The width is 22 cm and the length is 27 cm.

Extra: The sum three Extra: The sum three consecutive numbers is 87. Find consecutive numbers is 87. Find the numbers.the numbers.


Set up the equationSet up the equation11stst + 2 + 2ndnd + 3 + 3rdrd = sum = sum

x + (x+1) + (x+2) = 87x + (x+1) + (x+2) = 87 Solve the equationSolve the equation

3x + 3 = 873x + 3 = 87

x = 28x = 28

1st

2nd

3rd Sum

X

X + 1

87

On number is 28.What are the other two?The numbers are28, 29 and 30

X + 2

Extra: The sum three consecutive Extra: The sum three consecutive ODDODD numbers is 87. Find the numbers is 87. Find the numbers.numbers.



x + (x+2) + (x+4) = 87x + (x+2) + (x+4) = 87 Solve the equationSolve the equation

3x + 6 = 873x + 6 = 87

x = 27x = 27

1st

2nd

3rd Sum

X

X + 2

87

On number is 27.What are the other two?The numbers are27, 29 and 31

X + 4

Extra: The sum three consecutive Extra: The sum three consecutive EVENEVEN numbers is 204. Find the numbers is 204. Find the numbers.numbers.



x + (x+2) + (x+4) = x + (x+2) + (x+4) = 204204

Solve the equationSolve the equation

3x + 6 = 2043x + 6 = 204

x = 66x = 66

1st

2nd

3rd Sum

X

X + 2

204

On number is 66.What are the other two?The numbers are66, 68 and 70.

X + 4

The end!The end!

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Handout Solve the following applications. Draw a table or diagram when necessary