Problem
Li needs to solve the problem below for homework and decides to use matrices. Which matrix represents the proper set up for the problem? Tickets to the high school theater production of "Hamilton" cost \$23 for adults and \$15 for children. If the high school brings in \$3103 for a night and 138 tickets are sold, how many adult tickets and children tickets are sold? Choose the correct answer below. A. $\left[\begin{array}{rr|r}23 & 15 & 136 \\ 1 & 1 & 3103\end{array}\right]$ B. $\left[\begin{array}{rr|r}23 & 1 & 3103 \\ 1 & 15 & 136\end{array}\right]$ c. $\left[\begin{array}{rr|r}23 & 15 & 3103 \\ 1 & 1 & 136\end{array}\right]$ D. $\left[\begin{array}{rr|r}23 & 1 & 136 \\ 1 & 15 & 3103\end{array}\right]$
Solution
Step 1 ：Let's denote the number of adult tickets as A and the number of children tickets as C.
Step 2 ：The first equation represents the total income from the tickets sold: \(23A + 15C = 3103\).
Step 3 ：The second equation represents the total number of tickets sold: \(A + C = 138\).
Step 4 ：Therefore, the correct matrix representation of the system is: \[\left[\begin{array}{rr|r}23 & 15 & 3103 \\ 1 & 1 & 138\end{array}\right]\]
Step 5 ：So, the correct answer is \(\boxed{C}\).
