Question

The school that Kathryn goes to is selling tickets to a spring musical. On the first day

of ticket sales the school sold 12 senior citizen tickets and 14 student tickets for a total
of $132. The school took in $108 on the second day by selling 12 senior citizen tickets
and 10 student tickets. What is the price each of one senior citizen ticket and one
student ticket?

Answer 1

Senior citizen ticket = $4, student ticket = $6

Explanation:

To do this, form a system of equations where x = the cost for a senior citizen ticket and y = the cost for a student ticket.

Since 12 senior citizen tickets and 14 students tickets cost $132, you get

12x + 14y = 132.

Since 12 senior citizen tickets and 10 students tickets cost $108, you get

12x + 10y = 108.

You can subtract those two equations, so

12x + 14y = 132

-(12x + 10y = 108)

and you get

4y = 24

divide both sides by 4

y = 6

substituting into the equation 12x + 10y = 108,

12x + 10(6) = 108

12x + 60 = 108

subtract 60 from both sides

12x = 48

divide both sides by 12

x = 4

A senior citizen ticket costs $4 and a student ticket costs $6.