Percent of Change

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Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Percent of Change

Warm UpSolve.

1. 10% of what number is 6?

2. What percent of 20 is 8?

3. What is 80% of 60?

4. 50 is what percent of 200?

60

40%

48

25%

Percent of Change

Problem of the Day

A pair of $100 sneakers was on sale for 50% off. Then the store manager marked them down another 30%. She then discounted the price by 20%. What is the total discount as a percent of the original price?72%

Percent of Change

Learn to solve problems involving percent of change.

Percent of Change

Vocabulary

percent of changepercent of increasepercent of decrease

Percent of Change

A percent can be used to describe an amount of change. The percent of change is the amount, stated as a percent, that a number increases or decreases. If the amount goes up, it is a percent of increase. If the amount goes down, it is a percent of decrease.

You can find the percent of change by using the following formula.

Percent of change = amount of changeoriginal amount

Percent of Change

Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.

Additional Example 1A: Finding Percent of Change

65 is decreased to 38.65 – 38 = 27

percent of change = 2765

0.4153846

The percent of decrease is about 41.5%.

Find the amount of change.Substitute values into formula.Divide.

Write as a percent. Round.

When a number is decreased, subtract the new amount from the original amount to find the amount of change.

Helpful Hint

41.5%

Percent of Change

Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.

Additional Example 1B: Finding Percent of Change

41 is increased to 92.92 – 41 = 51

Percent of change =41

1.2439

The percent of increase is about 124.4%

Find the amount of change.

Substitute values into formula.Divide.

Write as a percent. Round. 124.4%

51

When a number is increased, subtract the original amount from the new amount.

Helpful Hint

Percent of Change

Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.

Check It Out: Example 1A

70 is decreased to 45.

70 – 45 = 25

percent of change = 2570

0.35714

The percent of decrease is about 35.7%.

Find the amount of change.

Substitute values into formula.

Divide.

Write as a percent. Round. 35.7%

Percent of Change

Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.

Check It Out: Example 1B

37 is increased to 56.

56 – 37 = 19

Percent of change =37

0.51351

The percent of increase is about 51.4%

Find the amount of change.

Substitute values into formula.

Divide.

Write as a percent. Round. 51.4%

19

Percent of Change

When you know the percent of change, you can use an equation to find the actual amount of change.

Percent of Change

The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. What is the sales price?

Additional Example 2: Using Percent of Change

Step 1: Find the amount of the discount d.

20% · 42.99 = d

0.20 · 42.99 = d

8.598 = d

$8.60 d

The amount of the discount is $8.60.

Think: 20% of $42.99 is what number?

Write the percent as a decimal.

Multiply.

Round to the nearest cent.

Percent of Change

The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. What is the sales price?

Additional Example 2 Continued

Step 2: Find the sale price.

regular price – amount of discount = sales price

The sale price is $34.39

$42.99 – $8.60 = $34.39

Percent of Change

The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price?

Check It Out: Example 2

Step 1: Find the amount of the discount d.

15% · 49.88 = d

0.15 · 49.88 = d

7.482 = d

$7.48 d

The amount of the discount is $7.48.

Think: 15% of $49.88 is what number?

Write the percent as a decimal.

Multiply.

Round to the nearest cent.

Percent of Change

Check It Out: Example 2 Continued

Step 2: Find the sale price.

regular price – amount of discount = sales price

The sale price is $42.40.

$49.88 – $7.48 = $42.40

The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price?

Percent of Change

A boutique buys hand-painted T-shirts for $12.60 each and sells them at a 110% increase in price. What is the retail price of the T-shirts?

Additional Example 3: Business Application

Step 1: Find the actual amount of increase.Think: 110% of $12.60 is what number?110% · 12.60 = n

1.10 · 12.60 = n

13.86 = n

Step 2: Find the selling price.

wholesale price + amount of increase = retail price

$12.60 + $13.86 = $26.46

The retail price of the hand-painted T-shirts is $26.46 each.

Write the percent as a decimal.

Multiply.

Percent of Change

Check It Out: Example 3

William makes T-shirts for $7.00 each and sells them after a price increase of 125%. What is the retail price of the T-shirts?Step 1: Find the actual amount of increase.

Think: 125% of $7.00 is what number?

125% · 7.00 = n

1.25 · 7.00 = n

8.75 = n

Step 2: Find the selling price.

The retail price of the T-shirts is $15.75 each.

Write the percent as a decimal.

Multiply.

wholesale price + amount of increase = retail price

$7.00 + $8.75 = $15.75

Percent of Change

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Percent of Change

Lesson Quiz

Find each percent of change.1. 10 is increased to 12.

2. 25 is increased to 45.

3. 10 is decreased to 1.

4. The regular price of a coat is $120. It is on sale for 25% off. What is the sale price?

5. A backpack that sells for $42 is on sale for 25% off. Find the sale price.

80%

20%

90%

$90

$31.50

Percent of Change

1. Identify the percent of change.

20 is increased to 22.

A. 10%

B. 20%

C. 30%

D. 40%

Lesson Quiz for Student Response Systems

Percent of Change

2. Identify the percent of change.

30 is increased to 54.

A. 30%

B. 54%

C. 75%

D. 80%

Lesson Quiz for Student Response Systems

Percent of Change

3. Identify the percent of change.

15 is decreased to 3.

A. 80%

B. 75%

C. 60%

D. 50%

Lesson Quiz for Student Response Systems

Percent of Change

4. The regular price of a camera is $140. A store offers 30% off on cameras. At this discounted rate, what is the sale price of a camera?

A. $110

B. $105

C. $98

D. $42

Lesson Quiz for Student Response Systems

Percent of Change

5. A camcorder that sells for $256 is on sale for 30% off. Identify the sale price.

A. $195.60

B. $179.20

C. $106.40

D. $76.80

Lesson Quiz for Student Response Systems