Basic Mathematics for College Students

6.2 Solving Percent Problems Using Percent Equations and Proportions 513

SECTION 6.2

Solving Percent Problems Using

Percent Equations and Proportions

The articles on the front page of the newspaper on the right illustrate three types of
percent problems.

Type 1In the labor article, if we want to know
how many union members voted to accept the
new offer, we would ask:

Type 2In the article on drinking water, if we
want to know what percent of the wells are
safe, we would ask:

Type 3In the article on new appointees, if we
want to know how many members are on the
State Board of Examiners, we would ask:

This section introduces two methods that can be used to solve the percent
problems shown above. The first method involves writing and solving percent
equations.The second method involves writing and solving percent proportions.If
your instructor only requires you to learn the proportion method, then turn to
page 520 and begin reading Objective 1.

METHOD 1: PERCENT EQUATIONS

6 is 75% of what number?

38 is what percent of 40?

What number is 84% of 500?

Objectives

PERCENT EQUATIONS

1 Translate percent sentences to

percent equations.

2 Solve percent equations to find

the amount.

3 Solve percent equations to find

the percent.

4 Solve percent equations to find

the base.

PERCENT PROPORTIONS

1 Write percent proportions.

2 Solve percent proportions to

find the amount.

3 Solve percent proportions to

find the percent.

4 Solve percent proportions to

find the base.

5 Read circle graphs.

1 Translate percent sentences to percent equations.

The percent sentenceshighlighted in blue in the introduction above have three things
in common.

• Each contains the word is.Here,iscan be translated as an symbol.


• Each contains the word of.In this case,ofmeans multiply.


• Each contains a phrase such as what numberor what percent.In other words,
  there is an unknown number that can be represented by a variable.
  These observations suggest that each percent sentence contains key words that
  can be translated to form an equation. The equation, called a percent equation,will
  contain three numbers (two known and one unknown represented by a variable), the
  operation of multiplication, and, of course, an symbol.

The Language of Mathematics The key words in a percent sentence

translate as follows:

• istranslates to an equal symbol .


• oftranslates to multiplication that is shown with a raised dot 


• what numberor what percenttranslates to an unknown number that is
  represented by a variable.

Circulation Monday, March 23 50 cents

Transit Strike Averted!

Drinking Water

38 of 40 Wells

Declared Safe

Labor: 84% of

500-member union

votes to accept

new offer

New Appointees

These six area residents

now make up 75% of the

State Board of Examiners