Q47. - Algebra 1

Question

FIND THE ERROR Maddie and Xavier are solving for the percent change if the original amount was \(25 and the new amount is \)28. Is either of them correct? Explain your reasoning.

Step-by-Step Solution

Answer

Xavier’s calculation is correct, the percentage change will be 12%.

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. Find the percentage change.

We are given that, the original amount is $25 and the new amount is $28.

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

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

Thus calculations done by Xavier are correct.