Question

Tickets for your schools play are $3 for students and $5 for non-students. On opening night 937 tickets are sold & $3943 is collected. How many tickets were sold to students and non students?

Answer 1

The school sold 371 tickets for students and 566 tickets for non-students.

Explanation:

Let's say that the number of tickets sold to students is `x` and the number of tickets sold to non-students is `y`.

You know that the school sold a total of 937 tickets, which means that you can write

`x + y = 937`

You also know that the total sum collected from selling these tickets is equal to $3943, so you can write

`3 * x + 5 * y = 3943`

Use the first equation to write `x` as a function of `y`

`x = 937 - y`

Plug this into the second equation and solve for `y` to get

`3 * (937 - y) + 5y = 3943`

`2811 - 3y + 5y = 3943`

`2y = 1132 implies y = 1132/2 = color(green)("566 tickets")`

This means that `x` will be equal to

`x = 937 - 566 = color(green)("371 tickets")`

The school thus sold 371 tickets for students and 566 tickets for non-students.