Question

At high school basketball game, the athletic department sold 250 tickets and brought in 837.50. Adult tickets cost $5 and student tickets cost $2.50. Write a system of equations for this situation.

Answer 1

The system of equations is:

`a+s = 250\\5a+2.50s = 837.50`

Here a is the number of adult tickets and s is the number of student tickets

Explanation:

We will use the given statements to make a system of equations for the given scenario.

First of all we have to decide which variables to be used.

Let a be the number of adult tickets and

Let s be the number of student tickets

So according to the statement that the department sold 250 tickets in total, the equation will be:

`a+s = 250`

This is equation one of the system of equations

According to the statement that cost of adult ticket is $5, total cost of adult tickets will be:
`5a`

According to the statement that cost of student ticket is $2.50, total cost of student tickets will be:
`2.50s`

The total earning was $837.50 so the second equation will be:

`5a+2.50s = 837.50`

Hence,

The system of equations is:

`a+s = 250\\5a+2.50s = 837.50`

Here a is the number of adult tickets and s is the number of student tickets