Basic Mathematics for College Students

ratio, , represent the same shaded portion of the

figure, they must be equal, and we can write

Recall from Section 5.2 that statements of this type stating that two ratios are

equal are called proportions.We call a percent proportion.The four terms of

a percent proportion are shown on the following page.

12  10050

1

2



50

100

10050

that , or 50% of the figure is shaded. The ratio is

called a percent ratio.

Since the amount-to-base ratio, , and the percent 12

10050 10050

520 Chapter 6 Percent

WHYThen we can translate the sentence into a percent equation and solve it to

find the unknown number of units in the complex.

SolutionAn occupancy rate of 88% means that 88% of the units are occupied.

Thus, the 198 units that are currently occupied are 88% of some unknown number

of units in the complex, and we can write:

is of

198  88%  x 198 is the amount, 88% is the percent,

and xis the base.

Now we solve the equation.

Write 88% as a decimal: 88% 0.88.

To undo the multiplication by 0.88 and isolate xon the right side,

divide both sides of the equation by 0.88.

To simplify the fraction on the right side of the

equation, remove the common factor of 0.88

from the numerator and denominator. On the left

side, divide 198 by 0.88.

The apartment complex has 225 units, of which 198, or 88%, are occupied.

225 x

198

0.88



0.88

1

x

0.88

1

198

0.88



0.88x

0.88

198 0.88x

198 88%x

198 88% what number?

225

(^88)  19800
 176
220
 176
440
 440
0
 
If you are only learning the percent equation method for solving percent
problems, turn to page 527 and pick up your reading at Objective 5.
METHOD 2: PERCENT PROPORTIONS
1 Write percent proportions.
Another method to solve percent problems involves
writing and then solving a proportion. To introduce this
method, consider the figure on the right. The vertical line
down its middle divides the figure into two equal-sized
parts. Since 1 of the 2 parts is shaded red, the shaded
portion of the figure can be described by the ratio. We
call this an amount-to-base(or part-to-whole) ratio.
Now consider the 100 equal-sized square regions
within the figure. Since 50 of them are shaded red, we say
12
The amount-to-base ratio  The percent ratio
50 of the 100 parts shaded:
50% shaded
2 parts
1 part shaded
    
Now TryProblem 81