Question

Kathryn's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 6 adult tickets and 11 student tickets for a total of $118. The school took in $156 on the second day by selling 12 adult tickets and 12 student tickets. What is the price of each adult ticket? What is the price of each student ticket?

Answer 1

Student tickets cost $8 and adult tickets cost $5.

Explanation:

12a + 12y = 156

6a + 11y = 118

We can multiply the second equation by -2 to try and cancel out the a variable.

`12a + 12y = 156\\-12a - 22y = -236\\\\-10y = -80\\y = 8`

Now that we know that the student tickets cost $8, we can substitute it into an equation to find the value of a, the adult tickets.

`12a + 12\cdot8 = 156\\12a+96=156\\12a=60\\a=5`

So, adult tickets cost $5 and student tickets cost $8.

Hope this helped!