Question

Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $12.50 per hour at her job, and Jack is paid $10 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $750 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?A. 40B. 20C. 25D. 30

Answer 1

Answer:

C. 25

Explanation:

Let the number of hours Jack can work = x

Let the number of hours Jane can work = y

If they do not want to work over 65 hours per week combined, then:

$\begin{gathered} x+y\le65 \\ \implies y\le65-x \end{gathered}$

Jack is paid $10 per hour at his.

Jane is paid $12.50 per hour at her job.

They need to make a minimum of $750 per week.

Therefore:

$10x+12.50y\le750$

To make it easier, we solve the system of equations below.

$\begin{gathered} y=65-x\ldots(1)\text{ \lbrack{}Substitute 1 into 2 below\rbrack} \\ 10x+12.50y=750\ldots(2) \\ 10x+12.50(65-x)=750 \\ 10x+812.50-12.50x=750 \\ -2.50x=750-812.50 \\ -2.50x=-62.50 \\ x=\frac{-62.50}{-2.50} \\ x=25 \end{gathered}$

Therefore, the maximum amount of hours that Jack can work per week according to these limits is 25 weeks.