Question

Janet is paid $0.50 more than Susan. They both worked 7 hours and their combined income was $112. a. At what rate does each get paid?b. Write an equation modeling the combined income of Janet and Susan.

Answer 1

The equation system is:

$\begin{gathered} S+0.5=J \\ 7S+7J=112 \end{gathered}$

Where S = Susan's salary per hour; J = Janet's salary per hour. The second equation means the combined income for 7 worked hours.

One substitute first equation into the second and solve for S:

$\begin{gathered} 7S+7(S+0.5)=112 \\ 7S+7S+3.5=112 \\ 14S=108.5 \\ S=7.75 \end{gathered}$

Then, we use the obtained value S to get Janet's salary:

$\begin{gathered} S+0.5=J \\ 7.75+0.5=J \\ J=8.25 \end{gathered}$

Answer a) Susan's salary = $7.75; Janet's salary = $8.25

Answer b)

$7S+7\mleft(S+0.5\mright)=112$