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Percent of Change

%change=[(final amount-original amount)/original amount] x 100%

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Percent of Change
License: CC BY-NC 3.0

In 2007, there were an estimated 80 million active users on Facebook. Between 2007 and 2015, Facebook’s active member base increased by 1,070%. That number continued to grow over time. As of March 2015, Facebook boasted 936 million active users. Approximately how many active users did Facebook have in 2015?

In this concept, you will learn to use the percent of change to find a new amount.

Using Percent of Change

If you are given the percent of increase or the percent of decrease and the original amount, you can find the new amount by using the following formula:

\begin{align*}\text{Amount of change} = \text{percent of change} \times \text{original amount}\end{align*}

Let’s apply this formula to a problem.

Find the new number when 75 is decreased by 40%.

First, find the amount of change.

\begin{align*}\begin{array}{rcl} \text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\ &=& 40 \% \times 75 \end{array}\end{align*}

Next, change the percent to a decimal and multiply to find the percent of change.

\begin{align*}\begin{array}{rcl} &=& 0.40 \times 75\\ &=& 30 \end{array}\end{align*}
Now, since the original number is being decreased, subtract the amount of change from the original number to find the new number.

\begin{align*}75 - 30 = 45\end{align*}

The answer is when 75 is decreased by 40%, the new number is 45.

Let’s look at another example.

Find the new number when 28 is increased by 125%.

First, find the amount of change.

\begin{align*}\begin{array}{rcl} \text{Amount of change} &=& \text{percent of change} \times \text{original amount} \\ &=& 125 \% \times 28 \end{array}\end{align*}

Next, change the percent to a decimal and multiply to find the percent of change.

\begin{align*}\begin{array}{rcl} &=& 1.25 \times 28 \\ &=& 35 \end{array}\end{align*}Now, since the original number is being increased, add the amount of change to the original number to find the new number.

\begin{align*}28 + 35 = 63\end{align*}

The answer is when 28 is increased by 125%, the new number is 63.

Examples

Example 1

Earlier, you were given a problem about Facebook and its number of active users.

The member base increased 1,070% between 2007, when it was 80 million active users, and 2015. How many active users did Facebook have in 2015?

First, find the amount of change.

\begin{align*}\begin{array}{rcl} \text{Amount of change} &=& \text{percent of change} \times \text{original amount} \\ &=& 1,070 \% \times 80 \text{ million} \end{array}\end{align*}

Next, change the percent to a decimal and multiply to find the percent of change.

\begin{align*}\begin{array}{rcl} &=& 10.70 \times 80 \text{ million} \\ &=& 856 \text{ million} \end{array}\end{align*}

Now, since the original number is being increased, add the amount of change to the original number to find the new number.

\begin{align*}80 \ \text{million} + 856 \ \text{million} = 936 \ \text{million}\end{align*}

The answer is the number of active Facebook users in 2015 was 936 million.

Example 2

The population of Westville grew from 25,000 to 27,000 in two years. What was the percent of increase for this period of time?

First, find the amount of the change by subtracting.

The amount of change is \begin{align*}27, 000 - 25, 000 = 2, 000\end{align*} 

Next, find the percent of the increase.

\begin{align*}\begin{array}{rcl} \text{Percent of increase or decrease} &=& \frac{\text{Amount of change}}{\text{Original amount}} \\ &=& \frac{2,000}{25,000}=\frac{2}{25} \\ &=& 0.08=8 \% \end{array}\end{align*}

The answer is the population increased 8% over this period of time.

Example 3

Find the new number when 45 is increased by 10%.

First, find the amount of change.

\begin{align*}\begin{array}{rcl} \text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\ &=& 10 \% \times 45 \end{array}\end{align*}

Next, change the percent to a decimal and multiply to find the percent of change.

\begin{align*}\begin{array}{rcl} &=&0.10 \times 45\\ &=& 4.5 \end{array}\end{align*}

Now, since the original number is being increased, add the amount of change to the original number to find the new number.

\begin{align*}45 + 4.5 = 49.5\end{align*}

The answer is when 45 is increased by 10%, the new number is 49.5.

Example 4

Find the new number when 80 is decreased by 15%.

First, find the amount of change.

\begin{align*}\begin{array}{rcl} \text{Amount of change} &=& \text{percent of change} \times \text{original amount} \\ &=& 15 \% \times 80 \end{array}\end{align*}

Next, change the percent to a decimal and multiply to find the percent of change.

\begin{align*}\begin{array}{rcl} &=& 0.15 \times 80 \\ &=& 12 \end{array}\end{align*}Now, since the original number is being decreased, subtract the amount of change from the original number to find the new number.

\begin{align*}80 - 12 = 68\end{align*}

The answer is when 80 is decreased by 15%, the new number is 68.

Example 5

Find the new number when 50 is increased by 25%.

First, find the amount of change.

\begin{align*}\begin{array}{rcl} \text{Amount of change} &=& \text{percent of change} \times \text{original amount}\\ &=& 25 \% \times 50 \end{array}\end{align*}

Next, change the percent to a decimal and multiply to find the percent of change.

\begin{align*}\begin{array}{rcl} &=& 0.25 \times 50 \\ &=& 12.5 \end{array}\end{align*}

Now, since the original number is being increased, add the amount of change to the original number to find the new number.

\begin{align*}50 + 12.5 = 62.5\end{align*}

The answer is when 50 is increased by 25%, the new number is 62.5.

Review

Find the percent of change and then use it to find a new amount.

  1. 25 decreased by 10%
  2. 30 decreased by 15%
  3. 18 decreased by 10%
  4. 30 decreased by 9%
  5. 12 decreased by 12%
  6. 90 decreased by 14%
  7. 200 decreased by 80%
  8. 97 decreased by 11%
  9. 56 decreased by 25%
  10. 15 decreased by 20%
  11. 220 decreased by 5%
  12. 75 decreased by 10%
  13. 180 decreased by 18%
  14. 1500 decreased by 12%
  15. 18,000 decreased by 24

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.16.

Resources

 

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Vocabulary

Percent Equation

The percent equation can be stated as: "Rate times Total equals Part," or "R% of Total is Part."

Percent of Decrease

The percent of decrease is the percent that a value has decreased by.

Percent of Increase

The percent of increase is the percent that a value has increased by.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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