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Solving Percents Problems. Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Solve. 1. 4 x = 90 2. 8 x = 96 3. 12 x = 180 4. 26 x = 182. 22.5. 12. 15. 7. 1. 3. Problem of the Day Rearrange the digits in . What - PowerPoint PPT Presentation
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7-8 Solving Percents ProblemsSolving Percents Problems
Warm Up
Lesson PresentationProblem of the Day
Lesson Quizzes
7-8 Solving Percents Problems
Warm UpSolve.
1. 4x = 902. 8x = 963. 12x = 1804. 26x = 182
22.512157
7-8 Solving Percents Problems
Problem of the DayRearrange the digits in . What fraction of the possible arrangements are true proportions?
26 = 1
3
13
7-8 Solving Percents Problems
Learn to solve problems involving percents.
7-8 Solving Percents Problems
Sloths may seem lazy, but their extremely slow movement helps to make them almost invisible to predators. Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day 16.5 hours is, you can use a proportion or an equation.
7-8 Solving Percents Problems
Proportion Method Equation Methodn
100 = 16.524
PartWhole
PartWhole What percent of 24 is 16.5?
n · 24 = 100 · 16.524n = 1,650
n = 68.75
n · 24 = 16.5n = 0.6875n = 68.75%
Sloths spend about 69% of the day sleeping!
7-8 Solving Percents Problems
Solve.
Additional Example 1A: Using Proportions to Solve Problems with Percents
What percent of 40 is 25?n
100= 25
40n · 40 = 100 · 25
40n = 2,50040n40
= 2,500 40
n = 62.525 is 62.5% of 40.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 40 to isolatethe variable.
7-8 Solving Percents Problems
Solve.
Additional Example 1B: Using Proportions to Solve Problems with Percents
15 is 25% of what number?25100
= 15n
n · 25 = 100 · 1525n = 1,50025n25
= 1,500 25
n = 6015 is 25% of 60.
Write a proportion.
Set the cross products equal.
Multiply.Divide each side by 25 to isolatethe variable.
7-8 Solving Percents Problems
Solve.
Check It Out: Example 1A
What percent of 50 is 10?n
100= 10
50n · 50 = 100 · 10
50n = 1,00050n50
= 1,000 50
n = 2010 is 20% of 50.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 50 to isolatethe variable.
7-8 Solving Percents Problems
Solve.
Check It Out: Example 1B
8 is 40% of what number?40100
= 8n
n · 40 = 100 · 840n = 80040n40
= 800 40
n = 208 is 40% of 20.
Write a proportion.
Set the cross products equal.
Multiply.Divide each side by 40 to isolatethe variable.
7-8 Solving Percents Problems
Solve.
Additional Example 2A: Using Equations to Solve Problems with Percents
35 is 28% of what number?35 = 28% · n35 = 0.28 · n35
0.28= 0.28 · n0.28
125 = n35 is 28% of 125.
Write an equation.Write 28% as a decimal.Divide each side by 0.28 to isolate the variable.
7-8 Solving Percents Problems
Solve.
Additional Example 2B: Using Equations to Solve Problems with Percents
What percent of 9 is 18?
18 = n · 9189 = n · 9
92 = n
200% = n18 is 200% of 9.
Write an equation.Divide each side by 9 to isolate the variable.Write the decimal as a percent.
7-8 Solving Percents Problems
Solve.Check It Out: Example 2A
36 is 24% of what number?36 = 24% · n36 = 0.24 · n
150 = n36 is 24% of 150.
Write an equation.Write 24% as a decimal.Divide each side by 0.24 to isolate the variable.
360.24= 0.24 · n
0.24
7-8 Solving Percents Problems
Solve.Check It Out: Example 2B
What percent of 6 is 36?
36 = n · 6366 = n · 6
66 = n
600% = n36 is 600% of 6.
Write an equation.Divide each side by 6 to isolate the variable.Write the decimal as a percent.
7-8 Solving Percents Problems
A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18?
Additional Example 3: Finding Sales Tax
n100 = 18
225n · 225 = 100 · 18
8% of $225 is $18. The sales tax is 8%.
Write a proportion.
Set the cross products equal.Multiply.
Restate the question: What percent of $225 is $18?
225n = 1800225n225 = 1800
225 Divide each side by 225.
n = 8
7-8 Solving Percents Problems
A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56?
Check It Out: Example 3
n100 = 56
800n · 800 = 100 · 56
7% of $800 is $56. The sales tax is 7%.
Write a proportion.
Set the cross products equal.Multiply.
Restate the question: What percent of $800 is $56?
800n = 5600800n800 = 5600
800 Divide each side by 800.
n = 7
7-8 Solving Percents Problems
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
7-8 Solving Percents ProblemsLesson Quiz
Solve.
1. 21 is 42% of what number? 2. What percent of 292 is 73?3. 112% of what number is 84?4. What percent of 1,340 is 13.4?5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate?
25%50
751%
6%
7-8 Solving Percents Problems
1. Solve. 19 is 38% of what number? A. 69B. 50C. 38D. 34
Lesson Quiz for Student Response Systems
7-8 Solving Percents Problems
2. What percent of 170 is 51? A. 25%B. 30%C. 40%D. 50%
Lesson Quiz for Student Response Systems
7-8 Solving Percents Problems
3. 128% of what number is 96? A. 25B. 50C. 75D. 96
Lesson Quiz for Student Response Systems
7-8 Solving Percents Problems
4. What percent of 1,520 is 15.2? A. 25%B. 15%C. 10%D. 1%
Lesson Quiz for Student Response Systems
7-8 Solving Percents Problems
5. A jeweler has a pendant on sale for $150. If the total cost of the pendant is $160.50, what is the sales tax rate?
A. 6%B. 7%C. 8%D. 9%
Lesson Quiz for Student Response Systems