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

Warm Up 1. Find 30% of 40. 2. Find 28% of 60. 12 Solve for x. 5. 20 is what percent of 80? 6. 36 is what percent of 30? 12 16.8 0.44 38 25% 120%

Objective Find percent increase and decrease.

Vocabulary percent change percent increase percent decrease discount markup

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.

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.

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%.

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 = 60% Write the answer as a percent. 75 to 30 is a decrease, so a change from 75 to 30 is a 60% decrease.

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

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

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

Example 2: Finding Percent Increase and Decrease 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%. Find 60% of 55. This is the amount of decrease. 0.60(55) = 33 55 – 33 = 22 It is a percent decrease so subtract 33 from the the original amount. 55 decreased by 60% is 22.

Check It Out! Example 2 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%. Find 40% of 10. This is the amount of decrease. 0.40(10) = 4 10 – 4 = 6 It is a percent decrease so subtract 4 from the the original amount. 10 decreased by 40% is 6.

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 = – A markup is an amount by which a wholesale price is increased. final price = wholesale cost markup + = % of

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.

Example 3A: Discounts 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.

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.

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 40% = x Write the answer as a percent. The discount is 40%

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

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%.

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 2 Method 1 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. 100% + 85% = 185% The selling price is 185% of the wholesale price, 7. 0.85(7) = 5.95 1.85(7) = 12.95 7 + 5.95 = 12.95 Find 185% of 7. This is the selling price. Add to 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.

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.

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 130% = x Write the answer as a percent. The markup was 130 percent.

Lesson Quiz: Part 1 Find each percent change. Tell whether it is a percent increase or decrease. 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%. 40% increase 22.5% decrease 80% decrease 168 56

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%