Question

Substitute teachers with Silvergrove School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday, 9 non-credentialed subs and 5 credentialed subs taught in the district. That cost the district $1140. Today, 6 non-credentialed subs and 5 credentialed subs taught, receiving $900 from the district. How much do subs get paid?subs with credentials get paid $ per day,Subs without credentials get paid $per day.

Answer 1

Given

9 non-credentialed subs and 5 credentialed subs taught in the district.

$1140

6 non-credentialed subs and 5 credentialed subs taught

$900

Procedure

x = subs with no credential

y = subs with credential

Equations

$\begin{gathered} 5x+9y=1140 \\ 5x+6y=900 \end{gathered}$

Solving the system

$\begin{gathered} 5x+9y=1140 \\ - \\ 5x+6y=900 \\ \\ 5x-5x+9y-6y=1140-900 \\ 3y=240 \\ y=\frac{240}{3} \\ y=80 \end{gathered}$

Now, for x

$\begin{gathered} 5x+6y=900 \\ 5x=900-6y \\ x=\frac{900-6y}{5} \\ x=\frac{900-6\cdot80}{5} \\ x=84 \end{gathered}$