 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 earning3.60 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.