1. Learn to solve problems involving percent of change.

2. Vocabulary
percent of change
percent of increase
percent of decrease

3. A percent can be used to describe an amount 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.
amount of change
original amount
Percent of change =

4. Additional Example 1A: Finding Percent of Change
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
65 is decreased to 38.
65 – 38 = 27
Find the amount of change. 27 65
Substitute values into
formula.
percent of change = 
Divide.
 41.5%
Write as a percent. Round.
The percent of decrease is about 41.5%.
When a number is decreased, subtract the new amount from the original amount to find the amount of change.
Helpful Hint

5. Additional Example 1B: Finding Percent of Change
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
41 is increased to 92.
92 – 41 = 51
Find the amount of change. 41 51
Substitute values into
formula.
Percent of change = 
Divide.
 124.4%
Write as a percent. Round.
The percent of increase is about 124.4%
When a number is increased, subtract the original amount from the new amount.
Helpful Hint

6. Check It Out: Example 1A
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
70 is decreased to 45.
70 – 45 = 25
Find the amount of change. 25 70
Substitute values into
formula.
percent of change = 
Divide.
 35.7%
Write as a percent. Round.
The percent of decrease is about 35.7%.

7. Check It Out: Example 1B
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
37 is increased to 56.
56 – 37 = 19
Find the amount of change. 37 19
Substitute values into
formula.
Percent of change = 
Divide.
 51.4%
Write as a percent. Round.
The percent of increase is about 51.4%

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

9. Additional Example 2: Using Percent of Change
The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sales price?
Step 1: Find the amount of the discount d.
20% · = d
Think: 20% of $42.99 is what number?
0.20 · = d
Write the percent as a decimal.
8.598 = d
Multiply.
$8.60  d
Round to the nearest cent.
The amount of the discount is $8.60.

10. Additional Example 2 Continued
The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sales price?
Step 2: Find the sale price.
regular price – amount of discount = sales price
$ – $ = $34.39
The sale price is $34.39

11. Step 1: Find the amount of the discount d.
Check It Out: Example 2
The regular price of a computer game is $ It is on sale for 15% off. What is the sales price?
Step 1: Find the amount of the discount d.
15% · = d
Think: 15% of $49.88 is what number?
0.15 · = d
Write the percent as a decimal.
7.482 = d
Multiply.
$7.48  d
Round to the nearest cent.
The amount of the discount is $7.48.

12. Check It Out: Example 2 Continued
The regular price of a computer game is $ It is on sale for 15% off. What is the sales price?
Step 2: Find the sale price.
regular price – amount of discount = sales price
$ – $ = $42.40
The sale price is $42.40.

13. Additional Example 3: Business Application
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?
Step 1: Find the actual amount of increase.
Think: 110% of $12.60 is what number?
110% · = n
1.10 · = n
Write the percent as a decimal.
13.86 = n
Multiply.
Step 2: Find the selling price.
wholesale price + amount of increase = retail price
$ $ = $26.46
The retail price of the hand-painted T-shirts is $26.46 each.

14. 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
Write the percent as a decimal.
8.75 = n
Multiply.
Step 2: Find the selling price.
wholesale price + amount of increase = retail price
$ $ = $15.75
The retail price of the T-shirts is $15.75 each.

15. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

16. 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 % off. Find the sale price.
20%
80%
90%
$90
$31.50