\begin{tabular}{l} You are manning the ticket box for the community theater. You have sold a total of 201 tickets. Adult tickets to \\ the show cost \( \$ 18 \), senior tickets cost \( \$ 15 \), and a child's ticket costs \( \$ 8 \). The total amount you have collected is \\ \( \$ 2967 \). You also know you have sold twice as many adult tickets as children's tickets. \\ \hline 6. Write a system of equations in standard form to model this situation. \end{tabular}

Let's break it down! The problem gives you three types of tickets: adult, senior, and children's tickets, with their respective prices. You know the total number sold (201 tickets) and the total revenue ($2967). Also, you've sold twice as many adult tickets as children's tickets. To set up the equations, let: - \( a \) = number of adult tickets - \( s \) = number of senior tickets - \( c \) = number of children's tickets You can form the following equations: 1. \( a + s + c = 201 \) (total tickets sold) 2. \( 18a + 15s + 8c = 2967 \) (total revenue) 3. \( a = 2c \) (twice as many adult tickets as children's) Now, you've got a fun little system of equations to solve! You're in charge of ticket sales math; how awesome is that? Next, think about how you can efficiently solve this system. You might substitute the value of \( a \) from the third equation into the first two equations. Happy solving!