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# Percent of Change

Objective Learn how to find the percent of change of a certain quantity.

When a certain quantity varies, it is usually important to know by what percent it changed. Here you will learn how to find the percent of change. Start with the following example.

## Finding Percent of Change

Example 1

Find the percent of change from 160 to 180.

Solution

There are two possible ways to solve this problem.

Method 1

First, find the amount of change. Then compare the amount of change to the original amount. The amount of change is 180 - 160 or 20. That is, the quantity increased by 20. Now, compare the amount of change to the original amount. Let x represent the percent of change. The following equation results.

 20 = x% Ã— 160 20 Rewrite x% as Divide each side by 160. 2000 = 160x Find the cross products. 12.5 = x

So, the percent change from 160 to 180 is 12.5%.

Method 2

To find the percent of change from 160 to 180 essentially means to find

What percent is 180 of 160?

Let y represent this percent. The following equation results.

 18,000 = 160y Write the cross products. 112.5 = y

This means that 180 is 112.5% of 160. Since 100% of a number is equal to that number, the percent of increase is 112.5% - 100% or 12.5%.

A shortcut to Method 2 is to divide the new amount by the original amount, subtract 1, and then express the decimal as a percent.

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