Question

State whether each percent of change is a percent of increase or a percent of decrease. Then find the percent of change. Round to the nearest whole percent.

$\begin{array}{l}\mathrm{Original}:41\\ \mathrm{New}:24\end{array}$

Short answer

The value of the percentage change is 41%.

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.

Step 2. Example of the percentage change.

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 3. Find the percentage change. 

We are given that

Original: 41

New: 24

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

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

$\begin{array}{l}\text{Decrease}=41-24=17\\ \%\text{change=r,then}\\ \frac{17}{41}=\frac{r}{100}\\ r=\frac{17}{41}\times 100\\ \text{r=\%change=0.4146}\times 100\\ \text{\%change=41.46}\\ \approx 41\text{\%}\end{array}$

Rounding answer off to the nearest whole number, the percentage change is 41%