Question

A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of

adults. There are half as many adults as there are children. If the total ticket sales was $ 2808, How many children,
students, and adults attended?

Answer 1

The attendance was 198 children, 90 students and 99 adults.

Explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

`5c+7s+12a=2808`

We also know that the children attendance doubles the adult attendance:

`c=2a`

The third equation is the seating capacity, which we assume is full:

`c+s+a=387`

We start by replacing variables in two of the equations:

`c=2a\\\\s=387-c-a=387-2a-a=387-3a`

Then, we solve the remaining equation for a:

`5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99`

Then, we solve for the other two equations:

`c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90`

The attendance was 198 children, 90 students and 99 adults.