We have to unknown values to find the number of day passes, we call x, and the number of weekend passes, we call y.
So we hhave two unknown variables we need two equations.
From the question we know the price of each ticket and the total sales, and also we know that they sold 201 more day passes than weekend passes.
In equation this is:
[tex]\begin{gathered} \text{Number of tickets:} \\ x=y+201 \\ \text{Total sales:} \\ 105\cdot x+111\cdot y=504,081 \end{gathered}[/tex]From the equations above, we can replace the x=y+201 into the second equation:
[tex]\begin{gathered} x=y+201 \\ 105\cdot(y+201)+111\cdot y=504081 \\ 105y+111y+105\cdot201=504081 \\ (105+111)y=504081-105\cdot201=504081-21105 \\ 216y=482976 \\ y=\frac{482976}{216}=2236 \\ x=y+201=2236+201=2437 \end{gathered}[/tex]They sold 2437 day passes and 2236 weekend passes
