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Understanding Percent Increase and Decrease in Holt Algebra

Learn how to calculate percent changes, identify increases and decreases, and solve problems involving discounts and markups using Holt Algebra methods. Practice quizzes included.

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Understanding Percent Increase and Decrease in Holt Algebra

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  1. Percent Increase and Decrease 2-10 Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

  2. Warm Up 1. Find 30% of 40. 2. Find 28% of 60. Solve for x. 3. 22 = x(50) 4. 17.2 = x(86) 5. 20 is what percent of 80? 6. 36 is what percent of 30? 12 16.8 0.44 38 25% 120%

  3. Objective Find percent increase and decrease.

  4. Vocabulary percent change percent increase percent decrease discount markup

  5. 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 be reduced.

  6. Example 1A: Finding Percent Increase and Decrease Find each percent change. Tell whether it is a percent increase or decrease. From 8 to 10 Simplify the numerator. Simplify the fraction. = 0.25 = 25% Write the answer as a percent. 8 to 10 is an increase, so a change from 8 to 10 is a 25% increase.

  7. Helpful Hint Before solving, decide what is a reasonable answer. For Example 1A, 8 to 16 would be a 100% increase. So 8 to 10 should be much less than 100%.

  8. Example 1B: Finding Percent Increase and Decrease Find the percent change. Tell whether it is a percent increase or decrease. From 75 to 30 Simplify the fraction. Simplify the numerator. = 0.6 Write the answer as a percent. = 60% 75 to 30 is a decrease, so a change from 75 to 30 is a 60% decrease.

  9. Check It Out! Example 1a Find each percent change. Tell whether it is a percent increase or decrease. From 200 to 110 Simplify the numerator. Simplify the fraction. = 0.6 Write the answer as a percent. = 60% 200 to 110 is an decrease, so a change from 200 to 110 is a 60% decrease.

  10. Check It Out! Example 1b Find each percent change. Tell whether it is a percent increase or decrease. From 25 to 30 Simplify the numerator. Simplify the fraction. = 0.20 Write the answer as a percent. = 20% 25 to 30 is an increase, so a change from 25 to 30 is a 20% increase.

  11. Check It Out! Example 1c Find each percent change. Tell whether it is a percent increase or decrease. From 80 to 115 Simplify the numerator. Simplify the fraction. = 0.4375 Write the answer as a percent. = 43.75% 80 to 115 is an increase, so a change from 80 to 115 is a 43.75% increase.

  12. Example 2: Finding Percent Increase and Decrease A. Find the result when 12 is increased by 50%. Find 50% of 12. This is the amount of increase. 0.50(12) = 6 It is a percent increase, so add 6 to the original amount. 12 + 6 =18 12 increased by 50% is 18. B. Find the result when 55 is decreased by 60%. Find 60% of 55. This is the amount of decrease. 0.60(55) = 33 It is a percent decrease so subtract 33 from the the original amount. 55 – 33 = 22 55 decreased by 60% is 22.

  13. Check It Out! Example 2 A. Find the result when 72 is increased by 25%. Find 25% of 72. This is the amount of increase. 0.25(72) = 18 It is a percent increase, so add 18 to the original amount. 72 + 18 =90 72 increased by 25% is 90. B. Find the result when 10 is decreased by 40%. Find 40% of 10. This is the amount of decrease. 0.40(10) = 4 It is a percent decrease so subtract 4 from the the original amount. 10 – 4 = 6 10 decreased by 40% is 6.

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

  15. Example 3: Discounts The entrance fee at an amusement park is $35. People over the age of 65 receive a 20% discount. What is the amount of the discount? How much do people over 65 pay? Method 1 A discount is a percent decrease. So find $35 decreased by 20%. Find 20% of 35. This is the amount of the discount. 0.20(35) = 7 35 – 7 = 28 Subtract 7 from 35. This is the entrance fee for people over the age of 65.

  16. Example 3A: Discounts Method 2 Subtract the percent discount from 100%. People over the age of 65 pay 80% of the regular price, $35. 100% – 20% = 80% 0.80(35) = 28 Find 80% of 35. This is the entrance fee for people over the age of 65. 35 – 28 = 7 Subtract 28 from 35. This is the amount of the discount. By either method, the discount is $7. People over the age of 65 pay $28.00.

  17. Helpful Hint Before solving, decide what is a reasonable answer. For example 3A, a 10% discount is $3.50 off. So a 20% discount would be more than $2 off.

  18. Example 3B: Discounts A student paid $31.20 for art supplies that normally cost $52.00. Find the percent discount . Think: 20.80 is what percent of 52.00? Let x represent the percent. $52.00 – $31.20 = $20.80 20.80 = x(52.00) Since x is multiplied by 52.00, divide both sides by 52.00 to undo the multiplication. 0.40 = x Write the answer as a percent. 40% = x The discount is 40%

  19. Check It Out! Example 3a A $220 bicycle was on sale for 60% off. Find the sale price. Method 2 Subtract the percent discount from 100%. 100% – 60% = 40% The bicycle was 60% off of 100% . 0.40(220) = 88 Find 40% of 220. By this method, the sale price is $88.

  20. Check It Out! Example 3b Ray paid $12 for a $15 T-shirt. What was the percent discount ? Think: 3 is what percent of 15? Let x represent the percent. $15 – $12 = $3 3 = x(15) Since x is multiplied by 15, divide both sides by 15 to undo the multiplication. 0.20 = x 20% = x Write the answer as a percent. The discount is 20%.

  21. Example 4: Markups The wholesale cost of a DVD is $7. The markup is 85%. What is the amount of the markup? What is the selling price? Method 1 Method 2 A markup is a percent increase. So find $7 increased by 85%. Add percent markup to 100% Find 85% of 7. This is the amount of the markup. The selling price is 185% of the wholesale price, 7. 100% + 85% = 185% 0.85(7) = 5.95 1.85(7) = 12.95 7 + 5.95 = 12.95 Add to 7. This is the selling price. Find 185% of 7. This is the selling price. 12.95  7 = 5.95 Subtract from 12.95. This is the amount of the markup. By either method, the amount of the markup is $5.95. The selling price is $12.95.

  22. Check It Out! Example 4 A video game has a 70% markup. The wholesale cost is $9. What is the selling price? Method 1 A markup is a percent increase. So find $9 increased by 70%. Find 70% of 9. This is the amount of the markup. 0.70(9) = 6.30 9 + 6.30 = 15.30 Add to 9. This is the selling price. The amount of the markup is $6.30. The selling price is $15.30.

  23. Check It Out! Example 4 What is the percent markup on a car selling for $21,850 that had a wholesale cost of $9500? 21,850 – 9,500 = 12,350 Find the amount of the markup. Think: 12,350 is what percent of 9,500? Let x represent the percent. 12,350 = x(9,500) Since x is multiplied by 9,500 divide both sides by 9,500 to undo the multiplication. 1.30 = x Write the answer as a percent. 130% = x The markup was 130 percent.

  24. Lesson Quiz: Part 1 Find each percent change. Tell whether it is a percent increase or decrease. 40% increase 1. from 20 to 28. 2. from 80 to 62. 3. from 500 to 100. 4. find the result when 120 is increased by 40%. 5. find the result when 70 is decreased by 20%. 22.5% decrease 80% decrease 168 56

  25. Lesson Quiz: Part 2 Find each percent change. Tell whether it is a percent increase or decrease. 6. A movie ticket costs $9. On Mondays, tickets are 20% off. What is the amount of discount? How much would a ticket cost on a Monday? 7. A bike helmet cost $24. The wholesale cost was $15. What was the percent of markup? $1.80; $7.20 60%

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