Question

The school that Mary goes to is selling tickets to a spring musical. On the first day of ticket sales

the school sold 6 adult tickets and 1 student ticket for a total of $82. The school took in $51 on
the second day by selling 3 adult tickets and 3 student tickets. What is the price each of one adult
ticket and one student ticket?

Answer 1

The cost of one adult ticket is $13, and the price of one student ticket is $4.

Explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the cost of an adult ticket

y is the cost of a student ticket.

6 adult tickets and 1 student ticket for a total of $82

This means that

`6x + y = 82`

`y = 82 - 6x`

The school took in $51 on the second day by selling 3 adult tickets and 3 student tickets.

This means that

`3x + 3y = 51`

Simplifying by 3

`x + y = 17`

Since
`y = 82 - 6x`

`x + 82 - 6x = 17`

`-5x = -65`

`5x = 65`

`x = (65)/(5) = 13`

`y = 82 - 6x = 82 - 6*13 = 82-78 = 4`

The cost of one adult ticket is $13, and the price of one student ticket is $4.