Basic Mathematics for College Students

6.2 Solving Percent Problems Using Percent Equations and Proportions 521

Percent Proportion

To translate a percent sentence to a percent proportion,use the following form:

Amount is to base as percent is to 100. Part is to whole as percent is to 100.

or

This is always 100 because percent

means parts per one hundred.

part

whole



percent

100

amount

base



percent

100

To write a percent proportion, you must identify 3 of the terms as you read the
problem. (Remember, the fourth term of the proportion is always 100.) Here are some
ways to identify those terms.

• The percentis easy to find. Look for the % symbol or the words what percent.


• The base(or whole) usually follows the word of.


• The amount(or part) is compared to the base (or whole).

Self Check 1

Translate each percent sentence

to a percent proportion.

a.What number is 33% of 80?

b.What percent of 55 is 6?

c.172% of what number is 4?

Now TryProblem 17













EXAMPLE (^1) Translate each percent sentence to a percent proportion.
a.What number is 12% of 64?
b.What percent of 88 is 11?
c.165% of what number is 366?
StrategyA percent proportion has the form. Since one of the
terms of the percent proportion is always 100, we only need to identify three terms
to write the proportion. We will begin by identifying the percent and the base in the
given sentence.
WHYThe remaining number (or unknown) must be the amount.
Solution
a.We will identify the terms in this order:

• First:the percent (next to the % symbol)


• Second:the base (usually after the word of)


• Last:the amount (the number that remains)

is of

b. of is

11

88



x

100

percent base amount

What 88 11?

x

64



12

100

amount percent base

What 12% 64?

amountbase percent 100