Question

Michelle and Julie are 17-year old twins. They have decided to save all of the money they earn so that they can buy a car to share. One week Michelle worked 8 hours and Julie worked 14 hours, and they saved $128. The next week Michelle worked 12 hours, Julie worked 16 hours, and they earned $162. a.) How much do Michelle and Julie earn per hour? b.) How much will they have saved after each works 100 hours?

Answer 1

Let x and y be the work per hour of M and J rspectively.

then,

`\begin{gathered} 8x+14y=128 \\ 12x+16y=162 \end{gathered}`

Multiply first equation by 3 and second equation by 2

`\begin{gathered} 24x+42y=384\ldots\text{.}\mathrm{}(3) \\ 24x+32y=324\ldots.(4) \end{gathered}`

Subtract eqn (4) from (3)

`\begin{gathered} 10y=60 \\ y=6 \end{gathered}`

Substitute for y in eqn (1).

`\begin{gathered} 8x+14*6=128 \\ 8x+84=128 \\ 8x=44 \\ x=5.5 \end{gathered}`