1. Percent Increase and Decrease
3.2
Percent Increase and Decrease
How do you use percents to describe change?

2. 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 =

3. 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

4. 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

5. 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%.

6. 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%

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

8. 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 actual amount of the discount.
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.

9. 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

10. Step 1: Find the actual amount of the discount.
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 actual amount of the discount.
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.

11. 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.

12. 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.

13. 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.

14. 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

15. ADDITIONAL EXAMPLE 2
The regular price of a scooter is $ It is on sale for $ What is the percent decrease from the regular price to the sale price of the scooter?
20%

16. ADDITIONAL EXAMPLE 3
A shoe sales associate earned $300 in August. In September she earned 8% more than she did in August. How much did she earn in September?
$324

17. ADDITIONAL EXAMPLE 1
The number of people signed up for a bus trip increased from 32 to 45. What is the percent increase? Round to the nearest percent.
41%

18. 3.2 LESSON QUIZ
7.4.D
Find each percent increase or decrease to the nearest percent. 1.
from 14 books to 40 books
186% increase 2.
from 72 points to 50 points
31% decrease

19. Find the new amount given the original amount and the percent of change.3.
$12; 20% increase
$14.40 4.
36 grams; 45% decrease
19.8 g 5.
If 48 eggs are used in the cafeteria today but the number expected to be used tomorrow is 30% less than that, how many eggs are expected to be used tomorrow? 34 6.
Priscilla currently reads 10 pages in her book each night. She wants to increase the number of pages by 30%. How many pages will Priscilla read each night after the increase? 13

20. On a grid draw a 4 × 4 square. Use the square and what you have learned about percent increase and percent decrease to determine what happens to the area of the square when the sides are increased by 50%. State by what percent the area increases. Then make a third square by decreasing the sides of the second square by 50%. State by what percent the area decreases. By what percent would you have had to change the sides of the 4 × 4 square to get the third square?

21. The area of the 4 × 4 square is 16 units2
The area of the 4 × 4 square is 16 units2. Increasing the sides by 50% makes a 6 × 6 square with an area of 36 units2. The area of the first square is increased by 125%. Decreasing the second square’s sides by 50% makes a 3 × 3 square with an area of 9 units2. The area of the second square is decreased by 75%. The sides of the original square could have been decreased by 25% to get the third square.

22. How do you use percents to describe change?
Sample answer:
Dividing the amount of the change by the original amount results in a percent increase or decrease.