6-5 Percent of Change Warm Up Problem of the Day Lesson Presentation Course 2 Warm Up Problem of the Day Lesson Presentation

6-5 Percent of Change Warm Up Solve. 1. 10% of what number is 6? Course 2 6-5 Percent of Change Warm Up Solve. 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%

6-5 Percent of Change Problem of the Day Course 2 6-5 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%

Course 2 6-5 Percent of Change Learn to solve problems involving percent of change.

Insert Lesson Title Here Course 2 6-5 Percent of Change Insert Lesson Title Here Vocabulary percent of change percent of increase percent of decrease

Course 2 6-5 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. amount of change original amount Percent of change =

Additional Example 1A: Finding Percent of Change Course 2 6-5 Percent 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. A. 65 is decreased to 38. Find the amount of change. 65 – 38 = 27 27 65 Substitute values into formula. percent of change =  0.4153846 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

Additional Example 1B: Finding Percent of Change Course 2 6-5 Percent of Change Additional Example 1B: Finding Percent of Change Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. B. 41 is increased to 92. 92 – 41 = 51 Find the amount of change. 41 51 Substitute values into formula. Percent of change =  1.2439 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

6-5 Percent of Change Try This: Example 1A Course 2 6-5 Percent of Change Try This: Example 1A Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. A. 70 is decreased to 45. Find the amount of change. 70 – 45 = 25 25 70 Substitute values into formula. percent of change =  0.35714 Divide.  35.7% Write as a percent. Round. The percent of decrease is about 35.7%.

6-5 Percent of Change Try This: Example 1B Course 2 6-5 Percent of Change Try This: Example 1B Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. B. 37 is increased to 56. 56 – 37 = 19 Find the amount of change. 37 19 Substitute values into formula. Percent of change =  0.51351 Divide.  51.4% Write as a percent. Round. The percent of increase is about 51.4%

Course 2 6-5 Percent of Change When you know the percent of change, you can use an equation to find the actual amount of change.

Additional Example 2A & 2B: Using Percent of Change Course 2 6-5 Percent of Change Additional Example 2A & 2B: Using Percent of Change The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. A. Find the actual amount of the discount. 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 discount is $8.60. B. Find the sale price. Subtract the discount from the regular price. $42.99 – $8.60 = $34.39 The sale price is $34.39

6-5 Percent of Change Try This: Example 2A & 2B Course 2 6-5 Percent of Change Try This: Example 2A & 2B The regular price of a computer game is $49.88. It is on sale for 15% off. A. Find the actual amount of the discount. 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 discount is $7.48. B. Find the sale price. Subtract the discount from the regular price. $49.88 – $7.48 = $42.40 The sale price is $42.40

Additional Example 3: Business Application Course 2 6-5 Percent of Change 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 selling price of the T-shirts? First find the actual amount of increase. Think: 110% of $12.60 is what number? 110% · 12.60 = n 1.10 · 12.60 = n Write the percent as a decimal. 13.86 = n Multiply. The amount of increase is $13.86. Now find the selling price. Think: retail price = wholesale price + amount of increase. p = $12.60 + $13.86 p = $26.46 The retail price of the hand-painted T-shirts is $26.46 each.

Insert Lesson Title Here Course 2 6-5 Percent of Change Insert Lesson Title Here Try This: Example 3 William makes T-shirts for $7.00 each and sells them after a price increase of 125%. What is the selling price of the T-shirts? First 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. The amount of increase is $8.75. Now find the selling price. Think: retail price = wholesale price + amount of increase. r = $7.00 + $8.75 r = $15.75 The retail price of the T-shirts is $15.75 each.

Insert Lesson Title Here Course 2 6-5 Percent of Change Insert Lesson Title Here 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. 120 is decreased to 90. 5. A backpack that sells for $42 is on sale for 25% off. Find the amount of discount and the sale price. 20% 80% 90% 25% $10.50, $31.50