Question

Find the percent decrease.

Last year, Sheila’s salary was \($42,000$. Because of furlough days, this year, her salary was \)$37,800$.

Short answer

If Sheila’s last year's salary was $$42000$and this year's salary is $$37800$then the percent decrease in salary is$10\%$.

Step-by-step solution

Step 1. Given information  

Sheila’s last year's salary was $$42000$.

Sheila’s this year's salary is $$37800$.

Step 2. Decreased amount

A decrease in salary is the difference between the salary in last year and this year

Consider D is the decrease in salary

decrease in salary is

$$\begin{gathered} D=42000-37800 \\ D=4200 \end{gathered}$$

So decrease in Sheila’s salary from last year to this year is $$4200$

Step 3. Percent decrease 

Consider Percent decrease is P

The decrease in salary is P percent of the salary of last year

$4200$ is P percent of $42000$

$$\begin{gathered} 4200=P\times 42000 \\ \frac{4200}{42000}=P \\ 0.1=P \\ P=10\% \end{gathered}$$

So percent decrease in salary of sheila from last year to this year is$10\%$

Step 4. Verification

$10\%$of $$42000$is

$0.1\times 42000=4200$

$10\%$of $$42000$is $$4200$

So $10\%$decrease in salary is correct.