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

2. 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%

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
= 60%
Write the answer as a percent.
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 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.

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 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.

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 fraction.
Simplify the numerator. =
= 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.

12. 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.
=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.

13. 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.
=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.

14. 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

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%.
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.

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 $ Find the percent discount .
Think: 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 to undo the multiplication.
0.40 = x
40% = x
Write the answer as a percent.
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. This is the discount from the original price.
220 – 88 = 142
By this method, the discount is $88. The sale price is $

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

24. 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

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%