Q18. - Algebra 1

Question

State whether the 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: 54             new: 45

Step-by-Step Solution

Answer

The percent of change is 17% decrease.

Step 1. Given information.

The original number is 54 and the new number is 45.

Step 2. to find the percent increase or decrease.

As original number is 54 and new number is 45.

Change between the both is:

New number $-$ Original number

So, width="93" style="max-width: none; vertical-align: -4px;" $45-54=-9$

It is a negative number

Therefore, the percent change is decrease.

Step 3. To find the percent change.

Let the percent change is $a\%$.

So,

$\begin{array}{l}\frac{9}{54}=\frac{a}{100}\\ \Rightarrow 54a=9\times 100\\ \Rightarrow a=\frac{9\times 100}{54}\\ \Rightarrow a=\frac{100}{6}\\ \Rightarrow a=16.67\end{array}$

Therefore, the whole percent is $17\%$.

Hence, the percent of change is width="34" height="19" style="max-width: none; vertical-align: -4px;" $17\%$ decrease.