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.

$\begin{array}{l}\mathrm{Original}:78\\ \mathrm{New}:125\end{array}$

Short answer

The value of the percentage change is 60%.

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 percentage increase or decrease. 

Since the new amount is larger than the original amount, there is a percent of the increase.

Step 3. Find the percentage change.

We are given that

Original: 78

New: 125

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:

$\begin{array}{l}\text{Decrease}=125-78=47\\ \%\text{change=r,then}\\ \frac{47}{78}=\frac{r}{100}\\ r=\frac{47}{78}\times 100\\ \text{r=\%change=0.6025}\times 100\\ \text{\%change=60.25}\\ \approx \text{60\%}\end{array}$

Rounding answer off to the nearest whole number, the percentage change is 60%