Question

The number of students at Franklin High School increased from 840 to 910 over a 5-year period. What was the percent of increase?

F 8.3%

G 14.0%

H 18.5%

J 92.3%

Short answer

The percentage increase is 8.3%, Option F is the correct choice.

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: 840

New: 910

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

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

$\begin{array}{l}\text{Change}=910-840=70\\ \%\text{change=r,then}\\ \frac{70}{840}=\frac{r}{100}\\ r=\frac{70}{840}\times 100\\ \text{r=\%change=0.0833}\times 100\\ \text{\%change=}8.333\\ \approx 8.3\text{\%}\end{array}$

Thus the percentage increase is 8.3%, and option F is the correct choice.