Basic Mathematics for College Students

6.2 Solving Percent Problems Using Percent Equations and Proportions 517

This is the equation to solve.

To undo the multiplication by 32 and isolate xon the

right side of the equation, divide both sides by 32.

To simplify the fraction on the right side of the

equation, remove the common factor of 32 from

the numerator and denominator. On the left

side, divide 14 by 32.

To write the decimal 0.4375 as a percent, multiply

it by 100 by moving the decimal point two places

to the right, and then insert a % symbol.

Thus, 14 is 43.75% of 32.

43.75%x

0 43.75%x

0.4375x

0.4375

x 32

1

32

1

14

32



x 32

32

14 x 32

0.4375

(^32)  14.0000
 12 8
1 20
 96
240
 224
160
 160
0

Using Your CALCULATOR Cost of an Air Bag
An air bag is estimated to add an additional $500 to the cost of a car. What
percent of the $16,295 sticker price is the cost of the air bag?
First, we translate the words of the problem into a percent equation.
of is
x  16,295  500 500 is the amount, xis the
percent, and 16,295 is the
Then we solve the equation. base.
To undo the multiplication by 16,295 and isolate xon the
left side, divide both sides of the equation by 16,295.
To simplify the fraction on the left side, remove the common
factor of 16,295 from the numerator and denominator.
To perform the division on the right side using a scientific calculator, enter the
following:
500 16295
This display gives the answer in decimal form. To change it to a percent, we
multiply the result by 100. This moves the decimal point 2 places to the right.
(See the display.) Then we insert a % symbol. If we round to the nearest tenth
of a percent, the cost of the air bag is about 3.1% of the sticker price.
3.068425898

  0.030684259

x

500

16,295

x16,295

16,295



500

16,295

x16,295 500

the cost of

the air bag?

the $16,295

sticker price

What

percent

    

EXAMPLE (^6) What percent of 6 is 7.5?
StrategyWe will look for the key words is, of,and what percentin the percent
sentence and translate them to mathematical symbols to form a percent equation.
WHYThen we can solve the equation to find the unknown percent.
Self Check 6
What percent of 5 is 8.5?
Now TryProblem 35