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

125% of 50.8 is what number?

Solution

Step 1:

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

Step 2:

The problem is re-written as 125% of 50.8 = x

This reduces to percent equation 125% × 50.8 = x

or 1.25 × 50.8 = x

Step 3:

Solving for x, x = 1.25×50.8 = 63.5

So, 125% of 50.8 is 63.5

Example 2

10.78 is what percent of 19.6?

Solution

Method 1

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 19.6 = 10.78

This reduces to percent equation x % × 19.6 = 10.78

or 0.0x × 19.6 = 10.78

Step 3:

Solving for x, x=(10.78×100)19.6=55

So, 55% of 19.6 is 39

Method 2

10.78 = x% × 19.6

10.78/19.6 = x=(x%×19.6)19.6=x

x = 0.55; converting the decimal to percent we get

x = 0.55 = 55%

Example 3

What is 90% of 218?

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 90% of 218 = x

This is reduced to percent equation 90% × 218 = x

or 0.90 × 218 = x

Step 3:

Solving for x, x = 0.90×218 = 196.2

So, 90% of 218 is 196.2