Question

The school that Imani goes to is selling tickets to a spring musical. On the first day of ticketsales the school sold 6 senior citizen tickets and 8 child tickets for a total of $122. The schooltook in $167 on the second day by selling 9 senior citizen tickets and 8 child tickets. WriteaSOE and solve it to find the price of a senior citizen ticket and the price of a child ticket

Answer 1

Define the system of equations to solve the problem

Take x as the price of a senior citizen ticket and y as the price of a child ticket

$\begin{gathered} 6x+8y=122 \\ 9x+8y=167 \end{gathered}$

Solve the system

$\begin{gathered} 6x+8y=122 \\ 8y=122-6x \\ 9x+8y=167 \\ 8y=167-9x \end{gathered}$$\begin{gathered} 122-6x=167-9x \\ 9x-6x=167-122 \\ 3x=45 \\ x=\frac{45}{3} \\ x=15 \end{gathered}$$\begin{gathered} 8y=122-6x \\ y=\frac{122-6x}{8} \\ y=\frac{122-6\cdot15}{8} \\ y=\frac{122-90}{8} \\ y=\frac{32}{8} \\ y=4 \end{gathered}$

The price of a senior citizen ticket is $15 and for child is $4