PERCENT INCREASE AND DECREASE

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. 

Percentage Change

Finding Percent Increase or Decrease

Example 1 : 

Find each percent change from 25 to 49.

Solution : 

25 to 49 is an increase,

percent change = (increase/original amount) x 100%

= [(49 - 25)/25] x 100%

= (24/25) x 100%

= 0.96 x 100%

= 96%

Percent change from 25 to 49 is a 96% increase.

Example 2 : 

Find each percent change from 50 to 45.

Solution : 

50 to 45 is a decrease,

percent change = (decrease/original amount) x 100%

= [(50 - 45)/50] x 100%

= (5/50) x 100%

= (1/10) x 100%

= 0.1 x 100% 

= 10%

Percent change from 50 to 45 is a 10% decrease.

Finding the Result of a Percent Increase or Decrease

Example 3 : 

Find the result when 30 is increased by 20%.

Solution : 

When 30 is increased by 20%, the resulting number is

= (100 + 20)% of 30

= 120% of 30

= (120/100) x 30

= 1.2 x 30

= 36

30 increased by 20% is 36.

Example 4 : 

Find the result when 65 is decreased by 80%.

Solution : 

When 65 is decreased by 80%, the resulting number is

= (100 - 80)% of 65

 = 20% of 65

= (20/100) x 65

= 0.2 x 65

= 13

65 decreased by 80% is 13.

Discounts and Markups

Example 5 : 

Admission to the museum is $8. Students receive a 15% discount. How much is the discount? How much do students pay?

Solution :

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

Method 2 :

Subtract percent discount from 100%.

100% - 15%  =  85%

Students pay 85% of the regular price, $8.

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 and students pay $6.80.

Example 6 : 

Christo used a coupon and paid $7.35 for a pizza that normally costs $10.50. Find the percent discount.

Solution :

$10.50 - $7.35  =  $3.15

Think : 3.15 is what percent of 10.50? Let x represent the percent.

3.15  =  x(10.50)

Because x is multiplied by 10.50, divide each side by 10.50 to undo the multiplication.

3.15/10.50  =  10.50x/10.50

0.3  =  x

Multiply 0.3 by 100 to convert it to a percent. 

0.3 ⋅ 100%  =  x

30%  =  x

The discount is 30%.

Example 7 : 

Jacob buys necklaces at a wholesale cost 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 I :

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

Method II :

Add percent markup to 100%.

100% + 75%  =  175%

The selling price is 175% of the wholesale price, $48.

Find 175% of 48. This is the selling price.

1.75(48)  =  84

Subtract the wholesale cost from 84. This is the amount of the markup.

84 - 48  =  36

By either method, the amount of the markup is $36 and the selling price is $84.

Example 8 : 

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

Think: 7 is what percent of 25? Let x represent the percent.

7  =  x(25)

Because x is multiplied by 25, divide each side by 25 to undo the multiplication.

7/25  =  25x/25

0.28  =  x

Multiply 0.28 by 100 to convert it to a decimal. 

0.28 ⋅ 100%  =  x

28%  =  x

The markup was 28%.

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