**Problem of the Week**

Problem C and Solution

Greta’s New Gig

**Problem**

Greta currently works 45 hours per week and earns a weekly salary of $729. She will soon be starting a new job where her salary will be increased by 10% and her hours reduced by 10%. How much more will she be earning per hour at her new job?

**Solution**

**Solution 1**

To calculate how much Greta earns per hour (i.e. her hourly rate of pay), divide her weekly salary by the number of hours worked.

Greta’s old hourly rate of pay is \(\$729\div 45\text{ h}=\$16.20\)/h.

\[\begin{aligned}
\text{New Weekly Salary }&=\text{Old Weekly Salary}+10\%\text{ of Old Weekly Salary}\\
&=\$729+0.1\times \$729\\
&=\$729+\$72.90\\
&=\$801.90\end{aligned}\]

\[\begin{aligned} \text{New Number of Hours Worked }&=\text{Old Hours Worked}-10\%\text{ of Old Hours Worked}\\ &=45\text{ h}-0.1\times 45\text{ h}\\ &=45\text{ h}-4.5\text{ h}\\ &=40.5\text{ h}\end{aligned}\]

Greta’s new hourly rate of pay is \(\$801.90\div 40.5\text{ h}=\$19.80\)/h.

The change in her hourly rate of pay is \(\$19.80\text{/h }-\$16.20\text{/h }=\$3.60\text{/h}\).

Therefore, Greta will be earning $3.60 more at her new job.

**Solution 2**

In the second solution we will use a more concise calculation. Greta’s new weekly salary is 10% more than her old weekly salary. So Greta will earn 110% of her old weekly salary. Greta’s hours will be reduced by 10%, so her new hours will be 90% of her old hours. To calculate her change in hourly rate we can take her new hourly rate and subtract her old hourly rate.

\[\begin{aligned}
\text{Change in Hourly Rate }&=\text{New Hourly Rate }-\text{ Old Hourly Rate}\\[-.5mm]
&=\text{New Salary}\div \text{New Hours Worked}-\text{Old Salary}\div \text{Old Hours Worked}\\
&=(\$729\times 1.10) \div (45 \times 0.9)-\$729 \div 45\\
&=\$801.90\div 40.5-\$729 \div 45\\
&=\$19.80\text{/h}-\$16.20\text{/h}\\
&=\$3.60\text{/h}\\\end{aligned}\] Therefore, Greta will be earning $3.60 more at her new job.