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Percent of Change: Solving Problems and Calculating Discounts

Learn how to solve problems involving percent of change and calculate discounts using the percent of increase or decrease. Understand the vocabulary related to percent of change and practice with examples.

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Percent of Change: Solving Problems and Calculating Discounts

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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%

  3. 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%

  4. Learn to solve problems involving percent of change.

  5. Vocabulary percent of change percent of increase percent of decrease

  6. 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 =

  7. 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%.

  8. 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%

  9. 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%.

  10. 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%

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

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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% · 12.60 = n 1.10 · 12.60 = n Write the percent as a decimal. 13.86 = n Multiply. 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.

  17. 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 $7.00 + $8.75 = $15.75 The retail price of the T-shirts is $15.75 each.

  18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  19. 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

  20. Lesson Quiz for Student Response Systems • Identify the percent of change. 20 is increased to 22. A. 10% B. 20% C. 30% D. 40%

  21. Lesson Quiz for Student Response Systems 2. Identify the percent of change. 30 is increased to 54. A. 30% B. 54% C. 75% D. 80%

  22. Lesson Quiz for Student Response Systems 3. Identify the percent of change. 15 is decreased to 3. A. 80% B. 75% C. 60% D. 50%

  23. Lesson Quiz for Student Response Systems 4. The regular price of a camera is $140. A store offers 30% off on cameras. At this discounted rate, what is the sale price of a camera? A. $110 B. $105 C. $98 D. $42

  24. Lesson Quiz for Student Response Systems 5. A camcorder that sells for $256 is on sale for 30% off. Identify the sale price. A. $195.60 B. $179.20 C. $106.40 D. $76.80

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