We have two variables the amount of full price tickets, we call x, and the discounted tickets, we call y.
From the problem, we know the total amount of tickets, 576=x+y, and the total money for the sales $5769, and the prices fro full ticket is $12.75 and for discounted ticket is $7.50.
So the equations are:
[tex]\begin{gathered} \text{The total amount of tickets:} \\ x+y=576 \\ \text{The total money:} \\ 12.75\cdot x+7.5\cdot y=5769 \end{gathered}[/tex]
Solving the above system of equations:
[tex]\begin{gathered} y=576-x \\ 12.75\cdot x+7.5\cdot(576-x)=5769 \\ 12.75\cdot x-7.5\cdot x+7.5\cdot576=5769 \\ (12.75-7.5)\cdot x+4320=5769 \\ 5.25\cdot x=5769-4320=1449 \\ x=\frac{1449}{5.25}=276 \\ y=576-276=300 \end{gathered}[/tex]
So, were sold 300 dicounted senior/student tickets
