Question

A movie theater has a seating capacity of 329. 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 $ 2388, How many children, students, and adults attended?

___ children attended.
___students attended.
____adults attended.

Answer 1

Down Below

Explanation:

The answer is actually

162 children

86 students

81 adults

162x5=810

86x7=602

81x12=972

I found the original problem and the total ticket sale was $2384.

So I wrote the answers for the original problem just in case!

Ty for your time!

Answer 2

170 children

74 students

85 adults

Explanation:

Given

Let:

`C = Children; S = Students; A = Adults`

For the capacity, we have:

`C + S + A = 329`

For the tickets sold, we have:

`5C + 7S + 12A = 2388`

Half as many as adults are children implies that:

`A = (C)/(2)`

Required

Solve for A, C and S

The equations to solve are:

`C + S + A = 329` -- (1)

`5C + 7S + 12A = 2388` -- (2)

`A = (C)/(2)` -- (3)

Make C the subject in (3)

`C = 2A`

Substitute
`C = 2A` in (1) and (2)

`C + S + A = 329` -- (1)

`2A + S + A = 329`

`3A + S = 329`

Make S the subject

`S = 329 - 3A`

`5C + 7S + 12A = 2388` -- (2)

`5*2A + 7S + 12A = 2388`

`10A + 7S + 12A = 2388`

`7S + 22A = 2388`

Substitute
`S = 329 - 3A`

`7(329 - 3A) + 22A = 2388`

`2303 - 21A + 22A = 2388`

`2303 +A = 2388`

Solve for A

`A = 2388 - 2303`

`A = 85`

Recall that:
`C = 2A`

`C = 2 * 85`

`C = 170`

Recall that:
`S = 329 - 3A`

`S = 329 - 3 * 85`

`S = 329 - 255`

`S = 74`

Hence, the result is:

`C = 170`

`S = 74`

`A = 85`