Q49. - Algebra 1

Question

WRITING IN MATH Explain how to find a percent of change between two values and how to determine whether the change is a percent of increase or decrease.

Step-by-Step Solution

Answer

The percent of increase or decrease can be determined by whether the final amount is increased or decreased with respect to the original amount.

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. Provide supportive examples.

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:

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

Note that percentages are written with respect to 100, in fact, the term ‘Per-Cent’ means proportionate to per 100 of the equated value. But this does not mean that percentage change cannot be more than or less than 100%.