Question

5) Sumalee's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 8 senior citizen tickets and 10 child tickets for a total of $156. The school took in $150 on the second day by selling 12 senior citizen tickets and 1 child ticket. Find the price of a senior citizen ticket and the price of a child ticket.

Answer 1

let x be senior tickets and y child tickets

$\begin{gathered} \begin{cases}8x+10y=156 \\ 12x+y=150\end{cases}\rightarrow\begin{cases}8x+10y=156 \\ -120x-10y=-1500\end{cases}\rightarrow \\ -112x=-1344\rightarrow x=\frac{1344}{112}=12 \end{gathered}$

so the senior ticket cost $12 and the child ticket cost $6

$12\cdot12+y=150\rightarrow y=150-144=6$