7-8 Solving Percents ProblemsSolving Percents Problems

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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