6-4 Solving Equations Containing Percents

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpSolve.

1. 4x = 90

2. 8x = 96

3. 12x = 180

4. 26x = 182

x = 22.5

x = 12

x = 15

Course 2

6-4 Solving Equations Containing Percents

x = 7

Problem of the Day

Rearrange the digits in . What

fraction of the possible arrangements are true proportions?

Course 2

6-4 Solving Equations Containing Percents

26

= 13

13

Learn to solve one-step equations containing percents.

Course 2

6-4 Solving Equations Containing Percents

Course 2

6-4 Solving Equations Containing Percents

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.

Course 2

6-4 Solving Equations Containing Percents

Proportion Method Equation Method

n100

= 16.524

PartWhole

PartWhole

What percent of 24 is 16.5?

n · 24 = 100 · 16.5

24n = 1,650

n = 68.75

n · 24 = 16.5

n = 0.6875

n = 68.75%

Sloths spend about 69% of the day sleeping!

Solve.

Additional Example 1A: Using Proportions to Solve Problems with Percents

Course 2

6-4 Solving Equations Containing Percents

A. 25 is what percent of 40?n

100= 25

40

n · 40 = 100 · 25

40n = 2,500

40n40

= 2,500 40

n = 62.5

25 is 62.5% of 40.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 40 to isolatethe variable.

Solve.

Additional Example 1B: Using Proportions to Solve Problems with Percents

Course 2

6-4 Solving Equations Containing Percents

B. 15 is 25% of what number?

25100

= 15n

n · 25 = 100 · 15

25n = 1,500

25n25

= 1,500 25

n = 60

15 is 25% of 60.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 25 to isolatethe variable.

Solve.

Try This: Example 1A

Course 2

6-4 Solving Equations Containing Percents

A. 10 is what percent of 50?n

100= 10

50

n · 50 = 100 · 10

50n = 1,000

50n50

= 1,000 50

n = 20

10 is 20% of 50.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 40 to isolatethe variable.

Solve.

Try This: Example 1B

Course 2

6-4 Solving Equations Containing Percents

B. 8 is 40% of what number?

40100

= 8n

n · 40 = 100 · 8

40n = 800

40n40

= 800 40

n = 20

8 is 40% of 20.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 25 to isolatethe variable.

Solve.

Additional Example 2A: Using Equations to Solve Problems with Percents

Course 2

6-4 Solving Equations Containing Percents

A. 35 is 28% of what number?

35 = 28% · n

35 = 0.28 · n

350.28

= 0.28 · n0.28

125 = n

35 is 28% of 125.

Write an equation.

Write 28% as a decimal.

Divide each side by 0.28 to isolate the variable.

Solve.

Additional Example 2B: Using Equations to Solve Problems with Percents

Course 2

6-4 Solving Equations Containing Percents

B. 18 is what percent of 9?

18 = n · 9

189

= n · 99

2 = n

200% = n

18 is 200% of 9.

Write an equation.Divide each side by 9 to isolate the variable.Write the decimal as a percent.

Solve.

Try This: Example 2A

Course 2

6-4 Solving Equations Containing Percents

A. 36 is 24% of what number?

36 = 24% · n

36 = 0.24 · n

150 = n

36 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 · n0.24

Solve.

Try This: Example 2B

Course 2

6-4 Solving Equations Containing Percents

B. 36 is what percent of 6?

36 = n · 6

366

= n · 66

6 = n

600% = n

36 is 600% of 6.

Write an equation.Divide each side by 6 to isolate the variable.Write the decimal as a percent.

Workers in Canada earn 10 vacation days, and workers in Finland earn 30 vacation days. What percent of the vacation days that workers in Canada earn do workers in Finland earn?

Additional Example 3: Social Studies Application

Course 2

6-4 Solving Equations Containing Percents

n · 10 = 30

n · 1010

= 3010

n = 3.0

Workers in Finland earn 300% of the number of vacation days that workers in Canada earn.

Write an equation.

Divide each side by 10 to isolate the variable.

Write the decimal as a percent.

Restate the question: What percent of 10 is 30?

n = 300

Workers in Canada earn 10 vacation days, and workers in Britain earn 20 vacation days. What percent of the vacation days that workers in Canada earn do workers in Britain earn?

Try This: Example 3

Course 2

6-4 Solving Equations Containing Percents

n · 10 = 20

n · 1010

= 2010

n = 2.0

Workers in Britain earn 200% of the number of vacation days that workers in Canada earn.

Write an equation.

Divide each side by 10 to isolate the variable.

Write the decimal as a percent.

Restate the question: What percent of 10 is 20?

n = 200

Lesson Quiz

1. 21 is 42% of what number?

2. 73 is what percent of 292?

3. 112% of what number is 84?

4. 13.4 is what percent of 1340?

5. An ad shows a DVD player on sale for 75% of its original price. If its original price was $242, what is the sale price?

25%

50

Insert Lesson Title Here

75

1%

Course 2

6-4 Solving Equations Containing Percents

$181.50