Page 482 - Basic College Mathematics with Early Integers

6.3 SOLVING PERCENT PROBLEMS USING PROPORTIONS Objectives

Write Percent Problems
as Proportions.
There is more than one method that can be used to solve percent problems. (See the
note at the beginning of Section 6.2.) In the last section, we used the percent equation. Solve Percent Problems.
In this section, we will use proportions.

Objective Writing Percent Problems as Proportions

To understand the proportion method, recall that 70% means the ratio of 70 to 100,
70
or .
100
Î shaded

70 7
70% = =
100 10

70
70% or shaded
100
70 7
Since the ratio is equal to the ratio , we have the proportion
100 10
7 70
= .
10 100
We call this proportion the “percent proportion.” In general, we can name the parts
of this proportion as follows:

Percent Proportion
amount percent
=
base 100 ; always 100
or
amount : a p ; percent
base : b = 100

When we translate percent problems to proportions, the percent, p, can be
identified by looking for the symbol % or the word percent.The base, b, usually fol-
lows the word of.The amount, a, is the part compared to the whole.

Part of Proportion How It’s Identified
Percent % or percent
Base Appears after of
Amount Part compared to whole

459