Learn to solve problems involving percent of change .

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. 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. amount of change original amount Percent of change =

4. Helpful Hint When a number is decreased, subtract the new amount from the original amount to find the amount of change. 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. Find the amount of change. 65 – 38 = 27 Substitute values into formula. 27 65 percent of change = Divide.  0.4153846  41.5% Write as a percent. Round. The percent of decrease is about 41.5%.

5. Helpful Hint When a number is increased, subtract the original amount from the new amount. 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 Substitute values into formula. 51 Percent of change = Divide.  1.2439 Write as a percent. Round.  124.4% The percent of increase is about 124.4%

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. Find the amount of change. 70 – 45 = 25 Substitute values into formula. 25 70 percent of change = Divide.  0.35714  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. Find the amount of change. 56 – 37 = 19 37 Substitute values into formula. 19 Percent of change = Divide.  0.51351 Write as a percent. Round.  51.4% 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 $42.99. It is on sale for 20% off. What is the sales price? Step 1: Find the amount of the discount d. 20% · 42.99 = d Think: 20% of $42.99 is what number? 0.20 · 42.99 = 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 $42.99. 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 $42.99 – $8.60 = $34.39 The sale price is $34.39

11. Check It Out: Example 2 The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price? Step 1: Find the amount of the discount d. 15% · 49.88 = d Think: 15% of $49.88 is what number? 0.15 · 49.88 = 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 $49.88. 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 $49.88 – $7.48 = $42.40 The sale price is $42.40.

13. 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. 20% 80% 90% $90 $31.50