Q63. - Algebra 1

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.

original: $\mathrm{\backslash (}72$, new: $\mathrm{\backslash )}60$

Step-by-Step Solution

Answer

The percentage of decreasing is $17\%$.

Step 1. Given information.

We have ‘original is $\mathrm{\$}72$ and new is $\mathrm{\$}60$’’.

To find the percent of the change is the percent of increase or decrease and then find the change nearest to the whole percent.

Step 2. Apply concept.

Firstly, we find the change between original and new data then find the percent of change by the formula.

Let $r$ be the percent of change then,

$\frac{\mathrm{Amount} \mathrm{of} \mathrm{change}}{\mathrm{Original} \mathrm{amount}}=\frac{r}{100}$

Step 3. Calculation.

Subtracting original from new:

$\mathrm{\$}60-\mathrm{\$}72=-\mathrm{\$}12$

So, it is negative then it states the percent of decrease.

Now, find the percentage of decreasing:

$\begin{array}{l}\frac{12}{72}=\frac{r}{100}\\ \Rightarrow r=\left(\frac{12}{72}\right)100\\ \Rightarrow r=\left(\frac{1}{6}\right)100\\ \Rightarrow r=16.67\end{array}$

Hence, the percentage of decreasing is $17\%$.