Question

Determine whether each percent of change is a percent of increase or a percent of decrease. Then find the percent of change.

$\begin{array}{l}\mathrm{Original}:24\\ \mathrm{New}:40\end{array}$

Short answer

The value of the percentage change is 66%.

Step-by-step solution

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

For example, if a person has 25 dollars and he gets 3 more dollars and now has 28 dollars, its percentage increase is calculated as shown:

$\begin{array}{l}\text{Increase}=28-25=3\\ \%\text{change=r,then}\\ \frac{3}{25}=\frac{r}{100}\\ r=\frac{3}{25}\times 100\\ =12\%\end{array}$

Step 2. Decide whether the percentage increases or decreases. 

Since the new amount is smaller than the original amount, there is a percent of decrease.

Step 3. Find the percentage change.

We are given that

$\begin{array}{l}\text{Original}:40\\ \text{New}:24\end{array}$

This is a percent of increase because the new amount is less than the original.

We find the amount of change. And calculate the percentage change as follows:

$\begin{array}{l}\text{Change}=40-24=16\\ \%\text{change=r,then}\\ \frac{16}{24}=\frac{r}{100}\\ r=\frac{16}{24}\times 100\\ \text{r=\%change=66\%}\end{array}$

Rounding answer off to the nearest whole number, the percentage change is