Applying the percent equation

Introduction

In this lesson, we solve problems involving percent equations. Percent problems can be reduced to equations and the unknown quantity is found by solving that equation

Consider the following example problems

Example 1

36 is what percent of 80?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as x% of 80 = 36

This is reduced to percent equation x% × 80 = 36

or 0.0x × 80 = 36

Step 3:

Solving for x, x = 36×100/80 = 45

So, 45% of 80 is 36

Example 2

65% of what is 39?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as 65% of x = 39

This reduces to percent equation 65% × x = 39

or 0.65 × x = 39

Step 3:

Solving for x, x = 39×100/65 = 60

So, 65% of 60 is 39

Example 3

42 is what percent of 140?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as x% of 140 = 42

This is reduced to percent equation x% × 140 = 42

or 0.0x × 140 = 42

Step 3:

Solving for x, x = 42×100/140 = 30

So, 30% of 140 is 42.