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# Percent of Change

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

When a certain quantity changes, it is often important to know by what percent it changed. For example, the statement there was an inflation of 5% in housing prices in the last year, means that the cost of housing went up 5% during the year. In this lesson you will learn how to compute the percent of change.

## Computing Percent of Change

There are two methods you should learn. Have a look at the following examples.

Example 1

Find the percent of change from 125 to 175.

Solution

Method 1 Find the difference of the quantities (the change) and compute what percent of the original quantity the difference is.

In this example, the difference of the quantities is 175 - 125 = 50. So the quantity increased by 50. We then need to find out what percent the difference 50 is of the original quantity 125.

Let x represent this percent.

50 is x % of 125

Substitute a multiplication sign for the word of, we have the equation 50 = x % Â· 125. Solve this equation for x.

So the percent change from 125 to 175 is 40%. Since the quantity increased from 125 to 175, we say that the percent increase is 40%.

Method 2 When you are asking for the percent change from 125 to 175, you are essentially asking what percent of 125 is 175. Let y represent this percent.

This says that 175 is 140% of 125. Since 100% of a number is equal to that number, the percent increase is 40%.

Notice that a shortcut to this calculation is simply to divide the new amount by the original amount.

Then subtract 1 and express the resulting decimal as a percent.

1.4 - 1 = 0.4

0.4 = 40%

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