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Algebra1 Percent Increase and Decrease

Algebra1 Percent Increase and Decrease. Warm Up. 1) What percent of 64 is 48?. 1) 75%. 2) 60%. 2) What percent of 90 is 54?. 3) What percent of 36 is 72?. 3) 200%. 4) What percent of 6 is 7.5?. 4) 125%. Applications of Percent.

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Algebra1 Percent Increase and Decrease

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  1. Algebra1Percent Increaseand Decrease CONFIDENTIAL

  2. Warm Up 1) What percent of 64 is 48? 1) 75% 2) 60% 2) What percent of 90 is 54? 3) What percent of 36 is 72? 3) 200% 4) What percent of 6 is 7.5? 4) 125% CONFIDENTIAL

  3. Applications of Percent A percent change is an increase or decrease given as a percent of the original amount. Percent increase describes an amount that has grown and percent decrease describes an amount that has been reduced. Percent Change percent change = amount of increase or decrease original amount , expressed as a percent CONFIDENTIAL

  4. Finding Percent Increase or Decrease Find each percent change. Tell whether it is a percent increase or decrease. A) from 25 to 56 SOLUTION: percent change = amount of increase original amount = 56 - 25 25 = 31 25 Simplify the numerator. = 0.96 = 96% Write the answer as a percent. CONFIDENTIAL

  5. B) from 25 to 17 SOLUTION: percent change = amount of decrease original amount = 25 - 17 25 = 8 25 Simplify the numerator. = 0.32 = 32% Write the answer as a percent. CONFIDENTIAL

  6. Now you try! Find each percent change. Tell whether it is a percent increase or decrease.: 1) from 200 to 110 1) 45% decrease 2) from 25 to 30 2) 20% increase CONFIDENTIAL

  7. Finding the Result of a Percent Increase or Decrease A) Find the result when 20 is increased by 40%. Find 40% of 20. This is the amount of the increase. 0.40 (20) = 8 It is a percent increase, so add 8 to the original amount. 20 + 8 = 28 20 increased by 40% is 28. B) Find the result when 75 is decreased by 60%. Find 60% of 75. This is the amount of the decrease. 0.60 (75) = 45 It is a percent decrease, so subtract 45 from the original amount. 75 - 45 = 30 75 decreased by 60% is 30. CONFIDENTIAL

  8. Now you try! 1) Find the result when 72 is increased by 25%. 1) 90 2) Find the result when 10 is decreased by 40%. 2) 6 CONFIDENTIAL

  9. Common applications of percent change are discounts and markups. discount = % of original price A discount is an amount by which an original price is reduced. final price = original price - discount markup = % of wholesale cost A markup is an amount by which a wholesale cost is increased. final price = wholesale cost + markup CONFIDENTIAL

  10. Discounts A) Admission to the museum is $8. Students receive a 15% discount. How much is the discount? How much do students pay? Method 1: A discount is a percent decrease. So find $8 decreased by 15%. Find 15% of 8. This is the amount of the discount. 0.15 (8) = 1.20 Subtract 1.20 from 8. This is the student price. 8 - 1.20 = 6.80 Next Page CONFIDENTIAL

  11. Method 2: Subtract percent discount from 100%. Students pay 85% of the regular price, $8. 100% - 15% = 85% Find 85% of 8. This is the student price. 0.85 (8) = 6.80 Subtract 6.80 from 8. This is the amount of the discount. 8 - 6.80 = 1.20 By either method, the discount is $1.20. Students pay $6.80. CONFIDENTIAL

  12. B) Christie used a coupon and paid $7.35 for a pizza that normally costs $10.50. Find the percent discount. 3.15 is what percent of 10.50? Let x represent the percent. $10.50 - $7.35 = $3.15 3.15 = x (10.50) 3.15 = x . (10.50) 10.50 10.50 Since x is multiplied by 10.50, divide both sides by 10.50 to undo the multiplication. 0.3 = x Write the answer as a percent. 30% = x The discount is 30%. CONFIDENTIAL

  13. Now you try! Solve: 1) A $220 bicycle was on sale for 60% off. Find the sale price. 1) $88 2) Ray paid $12 for a $15 T-shirt. What was the percent discount? 2) 20% CONFIDENTIAL

  14. Markups A) Kale buys necklaces at a wholesale price of $48 each. He then marks up the price by 75% and sells the necklaces. What is the amount of the markup? What is the selling price? Solution: Method 1: A markup is a percent increase. So find $48 increased by 75%. Find 75% of 48. This is the amount of the markup. 0.75 (48) = 36 Add to 48. This is the selling price. 48 + 36 = 84 Next Page CONFIDENTIAL

  15. Method 2: Add percent markup to 100%. The selling price is 175% of the wholesale price, $48. 100% + 75% = 175% Find 175% of 48. This is the selling price. 1.75 (48) = 84 Subtract from 84. This is the amount of the markup. 84 - 48 = 36 By either method, the amount of the markup is $36. The selling price is $84. CONFIDENTIAL

  16. B) Lars purchased a daily planner for $32. The wholesale cost was $25. What was the percent markup? Solution: Find the amount of the markup. 32 - 25 = 7 7 is what percent of 25? Let x represent the percent. 7 = x (25) 7 = x . (25) 25 25 Since x is multiplied by 25, divide both sides by 25 to undo the multiplication. 0.28 = x 28% = x Write the answer as a percent. The markup was 28%. CONFIDENTIAL

  17. Now you try! Solve: 1) A video game has a 70% markup. The wholesale cost is $9. What is the selling price? 1) $15.3 2) What is the percent markup on a car selling for $21,850 that had a wholesale cost of $9500? 2) 130% CONFIDENTIAL

  18. Some more examples A) A trader marks his goods 40% above cost price and allows a discount of 25% .What gain percent does he make? SOLUTION: Let the cost price be $100. Then marked price = $140. Discount = 25% of marked price = $140 × 25 = $35 100 Therefore, net selling price = Marked price – Discount = $(140 – 35) = $105 Therefore, gain = 5% Hence, the trader gains 5%. CONFIDENTIAL

  19. B) By allowing a discount of 10% on the marked price of an article, a dealer gains 8%. By what percent is the marked price above cost price? SOLUTION: Let the cost price be $100. Then, selling price = $108. When marked price $100, then $100 is the discount and $90 is the selling price. Thus, when selling price is $90, then marked price = $100. When selling price is $1, then marked price = $100 90 When selling price is $108, thenmarked price = $108 ×100= $120 90 Hence, the marked price is 20% above the cost price. CONFIDENTIAL

  20. Now you try! Solve: 1) A dealer marked his goods 35% above the cost price and allows a discount of 20% on the marked price. Find his gain or loss percent. 1)Gain = 8% CONFIDENTIAL

  21. Assessment 1) 80% of a number is the same as a --% decrease from that number. 1) 20% 2) Find the result when 40 is increased by 85%. 2) 74 3) Find the result when 60 is increased by 3%. 3) 78 4) What is the final price on a $185 leather jacket that is on sale for 40% off? 4) $111 CONFIDENTIAL

  22. Find each percent change. Tell whether it is a percent increase or decrease 5) 25 to 45 5) 80% increase 6) 10 to 8 6) 20% decrease 7) 400 to 300 7) 25% decrease CONFIDENTIAL

  23. 8) Robert finds a shirt on a sale rack. All items on the rack are 40% off. The price on his shirt is missing. When the clerk scans the bar code, he tells Robert that the sale price of shirt is $18. What percent of the original price is 18? 8) 60% 9) A can of soup had 480 mg of sodium per serving. The sodium was reduced to 360 mg per serving so that the soup could be advertised as “low sodium.” What was the percent change in sodium content? 9) 25% decrease 10) Last summer, Duncan charged $20 to mow a lawn in his neighborhood. This summer, he’ll charge $23. What is the percent increase in Duncan’s price? Show that your answer is reasonable. 10) 15% CONFIDENTIAL

  24. Let’s review Applications of Percent A percent change is an increase or decrease given as a percent of the original amount. Percent increase describes an amount that has grown and percent decrease describes an amount that has been reduced. Percent Change percent change = amount of increase or decrease original amount , expressed as a percent CONFIDENTIAL

  25. review Finding Percent Increase or Decrease Find each percent change. Tell whether it is a percent increase or decrease. A) from 25 to 56 SOLUTION: percent change = amount of increase original amount = 56 - 25 25 = 31 25 Simplify the numerator. = 0.96 = 96% Write the answer as a percent. CONFIDENTIAL

  26. Finding the Result of a Percent Increase or Decrease A) Find the result when 20 is increased by 40%. review Find 40% of 20. This is the amount of the increase. 0.40 (20) = 8 It is a percent increase, so add 8 to the original amount. 20 + 8 = 28 20 increased by 40% is 28. B) Find the result when 75 is decreased by 60%. Find 60% of 75. This is the amount of the decrease. 0.60 (75) = 45 It is a percent decrease, so subtract 45 from the original amount. 75 - 45 = 30 75 decreased by 60% is 30. CONFIDENTIAL

  27. review Common applications of percent change are discounts and markups. discount = % of original price A discount is an amount by which an original price is reduced. final price = original price - discount markup = % of wholesale cost A markup is an amount by which a wholesale cost is increased. final price = wholesale cost + markup CONFIDENTIAL

  28. review Markups A) Kale buys necklaces at a wholesale price of $48 each. He then marks up the price by 75% and sells the necklaces. What is the amount of the markup? What is the selling price? Solution: Method 1: A markup is a percent increase. So find $48 increased by 75%. Find 75% of 48. This is the amount of the markup. 0.75 (48) = 36 Add to 48. This is the selling price. 48 + 36 = 84 Next Page CONFIDENTIAL

  29. review Method 2: Add percent markup to 100%. The selling price is 175% of the wholesale price, $48. 100% + 75% = 175% Find 175% of 48. This is the selling price. 1.75 (48) = 84 Subtract from 84. This is the amount of the markup. 84 - 48 = 36 By either method, the amount of the markup is $36. The selling price is $84. CONFIDENTIAL

  30. review B) Lars purchased a daily planner for $32. The wholesale cost was $25. What was the percent markup? Solution: Find the amount of the markup. 32 - 25 = 7 7 is what percent of 25? Let x represent the percent. 7 = x (25) 7 = x . (25) 25 25 Since x is multiplied by 25, divide both sides by 25 to undo the multiplication. 0.28 = x 28% = x Write the answer as a percent. The markup was 28%. CONFIDENTIAL

  31. Some more examples review A) A trader marks his goods 40% above cost price and allows a discount of 25% .What gain percent does he make? SOLUTION: Let the cost price be $100. Then marked price = $140. Discount = 25% of marked price = $140 × 25 = $35 100 Therefore, net selling price = Marked price – Discount = $(140 – 35) = $105 Therefore, gain = 5% Hence, the trader gains 5%. CONFIDENTIAL

  32. You did a great job today! CONFIDENTIAL

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