Algebra Demystified 2nd Ed

Chapter 8 linear appliCaTionS 225

Increasing/Decreasing by a Percent

As consumers, we often see quantities being increased or decreased by some

percentage. For instance, a cereal box claims “25% More.” An item might be on

sale, its tag saying “Reduced by 40%.” We now learn how to interpret these

percentage changes. If we increase the quantity x by percentage p (the percent

written as a decimal number), the final quantity is xp+ x. If we decrease the

quantity x by percentage p, the final quantity is xp− x.

EXAMPLE

Compute.

80 increased by 20%

80 increased by 20% is xp+ x

80 +=(. 0208 )( 08 ) 01 += 696

24 increased by 35%

24 increased by 35% is 24 + (0.35)(24) = 24 + 8.4 = 32.4

36 increased by 250%

36 increased by 250% is 36 + (2.50)(36) = 36 + 90 = 126

64 decreased by 27%

64 decreased by 27% is 64 – (0.27)(64) = 64 – 17.28 = 46.72

PRACTICE

Compute.

1. 46 increased by 60% is __.


2. 78 increased by 125% is __.


3. 16 decreased by 30% is __.


4. 54 increased by 21.3% is ___.


5. 128 decreased by 8.16% is ___.


6. 15 increased by 0.03% is ____.


7. 24 decreased by 108.4% is ___.

✔SOLUTIONS

1. 46 increased by 60% is 46 + (0.60)(46) = 46 + 27.6 = 73.6


2. 78 increased by 125% is 78 + (1.25)(78) = 78 + 97.5 = 175.5


3. 16 decreased by 30% is 16 – (0.30)(16) = 16 – 4.8 = 11.2

EXAMPLE

Compute.

PRACTICE

Compute.