PERCENT OF CHANGE

Percents can be used to describe how an amount changes. The formula given below can be used to find how an amount changes in terms of percentage. 

The change may be an increase or a decrease.

Percent increase describes how much a quantity increases in comparison tothe original amount.

Percent decrease describes how much a quantity decreases in comparison to the original amount.

Examples

Example 1 : 

The price of a product is increased from $120 to $144. Find the increase in percent. 

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  144 - 120

=  24

Step 2 : 

Percentage change is 

=  (Amount of change / Original amount) x 100 %

=  (24 / 120) ⋅ 100%

=  0.2 ⋅ 100 %

=  20 %

So, the percent increase from $120 to $144 is 20%.

Example 2 : 

Find the increase in percent from 45 ft to 92 ft.

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  92 - 45

=  47

Step 2 : 

Percentage change is 

=  (Amount of change / Original amount) x 100 %

=  (47 / 45) ⋅ 100%

≈  1.0444 ⋅ 100 %

≈  104.44 %

≈  104 %

So, the percent increase from 45 ft to 92 ft is about 104%. 

Example 3 : 

Find the increase in percent from 74 hours to 85 hours.

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  85 - 74

=  11

Step 2 : 

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100 %

=  (11 / 74) ⋅ 100%

≈  0.1486 ⋅ 100 %

≈  14.86 %

≈  15 %

So, the percent increase from 74 hours to 85 hours is about 15%. 

Example 4 : 

Find the percent decrease from 96 inches to 36 inches.

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  96 - 36

=  60

Step 2 : 

Percentage change is  

=  (Amount of change / Original amount) x 100 %

=  (60 / 96) ⋅ 100%

=  0.625 ⋅ 100 %

=  62.5 %

So, the percent decrease from 96 inches to 36 inches is about 62.5%. 

Example 5 : 

Find the percent decrease from 3 ft to 24 inches.   

Solution :

Step 1 :

The given measures must be in same units. 

Convert 3 ft into inches. 

3 ft  =  3 ⋅ 12 inches

3 ft  =  36 inches

So, we need to find percent decrease from 36 inches to 24 inches.   

Step 2 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  36 - 24

=  12

Step 3 : 

Percentage change is 

=  (Amount of change / Original amount) x 100 %

=  (12 / 36) ⋅ 100%

≈  0.3333 ⋅ 100 %

≈  33.33 %

≈  33 %

So, the percent decrease from 3 ft to 24 inches is about 33%. 

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