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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 Course 2 6-6 Percent of Change 25% Wednesday February 1, 2012 Homework pg. 354 #7-18 2/01/12

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Learn to solve problems involving percent of change. 7.RP.2a-17.RP.2a-1 - Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table. EQ Give an example in which the amount of increase is greater than the original amount. What do you know about the percent? Course 2 6-6 Percent of Change

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

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

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Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. Additional Example 1A: Finding Percent of Change Course 2 6-6 Percent of Change 65 is decreased to 38. 65 – 38 = 27 percent of change = 27 65 0.4153846 The percent of decrease is about 41.5%. Find the amount of change. Substitute values into formula. Divide. Write as a percent. Round. When a number is decreased, subtract the new amount from the original amount to find the amount of change. Helpful Hint 41.5%

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Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. Additional Example 1B: Finding Percent of Change Course 2 6-6 Percent of Change 41 is increased to 92. 92 – 41 = 51 Percent of change = 41 1.2439 The percent of increase is about 124.4% Find the amount of change. Substitute values into formula. Divide. Write as a percent. Round. 124.4% 51 When a number is increased, subtract the original amount from the new amount. Helpful Hint

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Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. Check It Out: Example 1A: pg. 155 #1 Course 2 6-6 Percent of Change 70 is decreased to 45. 70 – 45 = 25 percent of change = 25 70 0.35714 The percent of decrease is about 35.7%. Find the amount of change. Substitute values into formula. Divide. Write as a percent. Round. 35.7%

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Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. Check It Out: Example 1B: Work it in try this #1 Course 2 6-6 Percent of Change 37 is increased to 56. 56 – 37 = 19 Percent of change = 37 0.51351 The percent of increase is about 51.4% Find the amount of change. Substitute values into formula. Divide. Write as a percent. Round. 51.4% 19

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

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The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. What is the sales price? Additional Example 2: Using Percent of Change Course 2 6-6 Percent of Change Step 1: Find the actual amount of the discount. 20% · 42.99 = d 0.20 · 42.99 = d 8.598 = d $8.60 d The amount of the discount is $8.60. Think: 20% of $42.99 is what number? Write the percent as a decimal. Multiply. Round to the nearest cent.

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The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. What is the sales price? Additional Example 2 Continued Course 2 6-6 Percent of Change Step 2: Find the sale price. regular price – amount of discount = sales price The sale price is $34.39 $42.99 – $8.60 = $34.39

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The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price? Check It Out: Example 2: Pg. 155 # 2 Course 2 6-6 Percent of Change Step 1: Find the actual amount of the discount. 15% · 49.88 = d 0.15 · 49.88 = d 7.482 = d $7.48 d The amount of the discount is $7.48. Think: 15% of $49.88 is what number? Write the percent as a decimal. Multiply. Round to the nearest cent.

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Check It Out: Example 2 Continued Course 2 6-6 Percent of Change Step 2: Find the sale price. regular price – amount of discount = sales price The sale price is $42.40. $49.88 – $7.48 = $42.40 The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price?

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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? Additional Example 3: Business Application Course 2 6-6 Percent of Change Step 1: Find the actual amount of increase. Think: 110% of $12.60 is what number? 110% · 12.60 = n 1.10 · 12.60 = n 13.86 = n Step 2: Find the selling price. wholesale price + amount of increase = retail price $12.60 + $13.86 = $26.46 The retail price of the hand-painted T-shirts is $26.46 each. Write the percent as a decimal. Multiply.

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Check It Out: Example 3: pg 155 try this 3 Insert Lesson Title Here Course 2 6-6 Percent of Change 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 8.75 = n Step 2: Find the selling price. The retail price of the T-shirts is $15.75 each. Write the percent as a decimal. Multiply. wholesale price + amount of increase = retail price $7.00 + $8.75 = $15.75

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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. 80% 20% Insert Lesson Title Here 90% $90 Course 2 6-6 Percent of Change $31.50

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Learn to solve problems involving percent of change. 7.RP.2a-17.RP.2a-1 - Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table. EQ Give an example in which the amount of increase is greater than the original amount. What do you know about the percent? Course 2 6-6 Percent of Change

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