Manny is looking to buy a new pair of sneakers. He really wants a designer pair, but they usually cost $165.00. Today, Manny walks past a store and notices that the shows he wants are on sale for $115.50. What is the percent of the decrease?

In this concept, you will learn to find the percent of decrease.

### Percent of Decrease

When you have an amount decreasing, you can always calculate the percent of decrease. The **percent of decrease** is the percent that a value decreases. To find the percent of decrease, divide the amount of decrease by the original amount and multiply by 100. In other words:

\begin{align*}\text{percent of decrease} = \frac{\text{amount of decrease}}{\text{original amount}} \times 100\end{align*}

Let’s look at an example where there is a percent of decrease.

A helicopter’s altitude went from 350 feet to 38 feet. This was a difference of 312 feet. By what percent did the altitude decrease?

Use the formula to find the percent of decrease.

\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{312}{350} \times 100 \\ \text{percent of decrease} &=& 89.14 \% \end{array}\end{align*}

The answer is 89.14%.

The helicopter has a percent of decrease in altitude by 89.14%.

### Examples

#### Example 1

Earlier, you were given a problem about Manny’s search for shoes.

The original price of the sneakers was $165 but Manny finds them on sale for $115.50. Manny wants to figure out the percent of the decrease.

First, find the difference.

\begin{align*}165-115.5=49.5\end{align*}

Next, use the formula to find the percent of decrease.

\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{49.5}{165} \times 100 \\ \text{percent of decrease} &=& 30 \% \end{array}\end{align*}

The answer is 30%.

Therefore, the sneakers are on sale 30% off.

#### Example 2

What is the percent of decrease from 2500 to 400?

First, find the difference.

\begin{align*}2500 - 400 =2100\end{align*}

Next, use the formula to find the percent of decrease.

\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{2100}{2500} \times 100 \\ \text{percent of decrease} &=& 84 \% \end{array}\end{align*}

The answer is 84%.

#### Example 3

Find each percent of decrease from 80 to 30.

First, find the difference.

\begin{align*}80 - 30=50\end{align*}

Next, use the formula to find the percent of decrease.

\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{50}{80} \times 100 \\ \text{percent of decrease} &=& 62.5 \% \end{array}\end{align*}

The answer is 62.5%.

#### Example 4

Find each percent of decrease from 90 to 40.

First, find the difference.

\begin{align*}90-40=50\end{align*}

Next, use the formula to find the percent of decrease.

\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{50}{90} \times 100 \\ \text{percent of decrease} &=& 55.6 \% \end{array}\end{align*}

The answer is 55.6%.

#### Example 5

Find each percent of decrease from 130 to 100.

First, find the difference.

\begin{align*}130-100=30\end{align*}

Next, use the formula to find the percent of decrease.

\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{30}{130} \times 100 \\ \text{percent of decrease} &=& 23.1 \% \end{array}\end{align*}

The answer is 23.1%.

### Review

Calculate the percent of decrease. You may round to the nearest whole percent.

- From 74 to 35, a decrease of 39
- From 576 to 476, a decrease of 100
- From 200 to 175, a decrease of 25
- From 150 to 100, a decrease of 50
- From 325 to 290, a decrease of 35
- From 45 to 18, a decrease of 27
- From 19 to 1, a decrease of 18
- From 22 to 10
- From 34 to 20
- From 230 to 220
- From 350 to 250
- From 700 to 350
- From 130 to 7
- From 890 to 700

### Review (Answers)

To see the Review answers, open this PDF file and look for section 5.11.