1. THESE SHOULD NOT BE DIFFICULT FOR YOU: 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? 16.8 12 0.2 0.44 25% 120%

2. Percent Increase and Percent Decrease

3. Find percent increase and decrease. Objective

4. Percent of Increase and Decrease

5. Percent change is the ratio of the amount of change to the original amount. Percent increase describes how much the original amount increases. Percent decrease describes how much the original amount decreases. amount of change original amount percent change =

6. Find the percent increase or decrease from 16 to 12. Is this percent an increase or decrease? 16 – 12 = 4First find the amount of change. Think: What percent is 4 of 16? amount of decrease original amount 4 16 Set up the ratio.

7. Continued = 25% Write as a percent. Reduce the fraction or find the decimal form. 4 16 From 16 to 12 is a 25% decrease. = 1 4

8. Find the percent of increase or decrease from 15 to 20. Try This: Is this percent an increase or decrease? 20 – 15 = 5First find the amount of change. Think: What percent is 5 of 15? amount of increase original amount 5 15 Set up the ratio.

9. Continued = 33 1 %Write as a percent. = 0.33…Find the decimal form. 5 15 From 15 to 20 is a 33 % increase. Reduce the fraction if possible. 1 3 3 3 1

10. Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the sale price? Percent Decrease $450  20%First find 20% of $450. $450  0.20 = $9020% = 0.20 The amount of decrease is $90. Think: The reduced price is $90 less than $450. $450 – $90 = $360Subtract the amount of decrease. The sale price of the DVD player was $360.

11. Mr. Olsen has a computer business in which he sells everything at 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price? Percent Increase $85  40% First find 40% of $85. $85  0.40 = $3440% = 0.40 The amount of increase is $34. Think: The retail price is $34 more than $85. $85 + $34 = $119 Add the amount of increase. The retail price of this printer will be $119.

12. 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.

13. Find each percent change. Tell whether it is a percent increase or decrease. From 8 to 10 = 0.25 = 25% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 8 to 10 is an increase, so a change from 8 to 10 is a 25% increase.

14. 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%.

15. From 75 to 30 = 0.6 = 60% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 75 to 30 is a decrease, so a change from 75 to 30 is a 60% decrease. Find the percent change. Tell whether it is a percent increase or decrease.

16. From 200 to 110 = 0.45 = 45% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 200 to 110 is a decrease, so a change from 200 to 110 is a 45% decrease. Find each percent change. Tell whether it is a percent increase or decrease.

17. From 25 to 30 = 0.20 = 20% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 25 to 30 is an increase, so a change from 25 to 30 is a 20% increase. Find each percent change. Tell whether it is a percent increase or decrease.

18. From 80 to 115 = 0.4375 = 43.75% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 80 to 115 is an increase, so a change from 80 to 115 is a 43.75% increase. Find each percent change. Tell whether it is a percent increase or decrease.

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

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

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

22. 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%. 0.20(35) = 7 Find 20% of 35. This is the amount of the discount. 35 – 7 = 28 Subtract 7 from 35. This is the entrance fee for people over the age of 65.

23. Method 2 Subtract the percent discount from 100%. 100% – 20% = 80% People over the age of 65 pay 80% of the regular price, $35. 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.

24. 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.

25. A student paid $31.20 for art supplies that normally cost $52.00. Find the percent discount. $52.00 – $31.20 = $20.80 Think: 20.80 is what percent of 52.00? Let x represent the percent. The discount is 40%

26. 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. This is the discount from the original price. 220 – 88 = 142 By this method, the discount is $88. The sale price is $142.00.

27. Ray paid $12 for a $15 T-shirt. What was the percent discount ? $15 – $12 = $3 Think: 3 is what percent of 15? Let x represent the percent. The discount is 20%.

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

29. 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%. 0.70(9) = 6.30 Find 70% of 9. This is the amount of the markup. 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.

30. 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 The markup was 130 percent. Think: 12,350 is what percent of 9,500? Let x represent the percent.