1. Notes 29
Percent of Change
6-4

2. Vocabulary
Percent of change- the amount, stated as a percent, that a number increases or decreases.
Percent of increase- when the amount of change goes up.
Percent of decrease- when the amount of change goes down.

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.

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.

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. 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?

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?