Answer:
[tex]\textsf{Roxy's annual income from her new employer before taxes will be $\boxed{\$62,400}$}\;.[/tex]
[tex]\textsf{Her bimonthly pay before taxes will be $\boxed{\$2,600}$}\;.[/tex]
[tex]\textsf{To reach Roxy's yearly pretax income goal of \$63,300, she will need to}\\\textsf{dog sit at least $\boxed{12}$ times}\;.[/tex]
Step-by-step explanation:
Given information:
- Pay = $30 per hour
- Number of hours worked per week = 40
- Number of weeks worked per year = 52
Therefore, Roxy's annual income before taxes will be:
[tex]\begin{aligned}\implies\textsf{Annual income}&=\sf pay\:per\;hr \times hours\;per\;wk \times weeks\;per\;yr\\& = \$30 \times 40 \times 52\\& = \$62,400\end{aligned}[/tex]
There are 12 months in a year.
If Roxy is paid bi-monthly, then she will be paid in 24 equal payments during the year. Therefore, her bi-monthly pay before taxes is:
[tex]\begin{aligned}\implies\textsf{Bi-monthly pay}&=\sf Annual\:pay \div 24\\& = \$62,400 \div 24\\&=\$2,600\end{aligned}[/tex]
Given:
- Roxy earns $75 each time she dog sits on the weekend.
Let x be the number of times she will need to dog sit. Therefore:
[tex]\begin{aligned}\implies \textsf{Annual pay}+\textsf{Dog sitting} & \geq 63300\\62400+75x& \geq 63300\\62400+75x-62400& \geq 63300-62400\\75x& \geq 900\\\dfrac{75x}{75}& \geq \dfrac{900}{75}\\x& \geq 12\end{aligned}[/tex]
Therefore, Roxy will need to dog sit at least 12 times to reach her yearly pretax income goal of $63,300.
