\begin{tabular}{l}\( \qquad \begin{array}{l}\text { 7. A local theater sold tickets for their fall play. On } \\ \text { Saturday night, they made } \$ 125 \text { in presales and sold } 120 \\ \text { tickets at the door. For the Saturday night show, they } \\ \text { earned } \$ 180 \text { in presales and sold } 110 \text { tickets at the door. } \\ \text { If the theater earned the same amount each night, what } \\ \text { is the cost per ticket? }\end{array} \) \\ \hline\end{tabular}

To find the cost per ticket, we first need to determine the total earnings for each night. On the first Saturday night, the theater made \$125 in presales and sold 120 tickets at the door, resulting in a total earning of \(125 + 120x\). For the second Saturday night, it earned \$180 in presales and sold 110 tickets, bringing the total to \(180 + 110y\). Since they earned the same amount each night, we can set the equations equal to each other: \[125 + 120x = 180 + 110y\] Now we need to rewrite it since we're looking for the ticket price (\(x\) or \(y\)). By simplifying and solving for \(x\) (assuming both ticket prices are equal), we can easily derive the ticket price. Now you can have fun figuring out the ticket price with the equation. One common mistake in this kind of problem is forgetting to pay attention to the presales versus door sales. Always double-check what comprises the total earnings! Balancing both the presales and door sales ensures you capture the whole earning picture, and it's essential for finding that elusive ticket price!