# 6.16: Percent of Change

**Basic**Created by: CK-12

**Practice**Percent of Change

Have you ever had to go to work when it was very cold?

Jenny put on her parka and headed to work at the candy store. At noon the temperature was \begin{align*}40^\circ F\end{align*}. At 6:00 P.M. the temperature dropped to \begin{align*}32^\circ F\end{align*}.

What was the percent of change in the temperature?

**This Concept is about using a percent of change to find a new amount. Use what you learn to figure out this Concept.**

### Guidance

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

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

Let’s apply this to a problem.

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

**First find the amount of change.**

\begin{align*}\text{Amount of change} & = \text{percent of change} \times \text{original amount}\\ & = 40 \% \times 75\\ & = 0.40 \times 75\\ & = 30\end{align*}

**Since the original number is being decreased, we subtract the amount of change from the original number to find the new number.** \begin{align*}75 - 30 = 45\end{align*}

**When 75 is decreased by 40%, the new number is 45.**

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

**First find the amount of change.**

\begin{align*}\text{Amount of change} & = \text{percent of change} \times \text{original amount}\\ & = 125 \% \times 28\\ & = 1.25 \times 28\\ & = 35\end{align*}

**Since the original number is being increased, we add the amount of change to the original number to find the new number.** \begin{align*}28 + 35 = 63\end{align*}

**When 28 is increased by 125%, the new number is 63.**

Now it's your turn to try a few. Find each new amount.

#### Example A

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

**Solution: \begin{align*}49.5\end{align*}**

#### Example B

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

**Solution:\begin{align*}68\end{align*}**

#### Example C

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

**Solution:\begin{align*}62.5\end{align*}**

Here is the original problem once again.

Jenny put on her parka and headed to work at the candy store. At noon the temperature was \begin{align*}40^\circ F\end{align*}. At 6:00 P.M. the temperature dropped to \begin{align*}32^\circ F\end{align*}.

What was the percent of change in the temperature?

**First, figure out the amount of the change.**

The amount of change is \begin{align*}40 - 32 = 8.\end{align*}

\begin{align*}\text{Percent of increase or decrease} & = \frac{\text{Amount of change}}{\text{Original amount}}\\ & = \frac{8}{40} = \frac{1}{5} = 0.20 = 20 \%\end{align*}

**The temperature decreased by 20%.**

### Vocabulary

Here are the vocabulary words used in this Concept.

- Percent of Increase
- the percent that a price or cost or number has increased.

- Percent of Decrease
- the percent that a price or cost or number has decreased.

### Guided Practice

Here is one for you to try on your own.

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?

**Answer**

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*}\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{align*}

**The population increased 8% over this period of time.**

### Video Review

Here is a video for review.

- This is a James Sousa video on the percent of change.

### Practice

Directions: 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%

Percentage Change Formula

positive

percent change would thus be an**increase**, while a

**negative**change would be a

**decrease.**

Percent Equation

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

Here you'll learn to use percent of change to find a new amount.

## Concept Nodes:

Percentage Change Formula

positive

percent change would thus be an**increase**, while a

**negative**change would be a

**decrease.**

Percent Equation

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