Question

A movie theater has a seating capacity of 271. 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 $
1974, How many children, students, and adults attended?
children attended.
students attended.
adults attended.

Answer 1

Children attended = 154

Students attended = 40

Adults attended = 77

Explanation:

Seating capacity = 271

Charges for each children ticket = $5

Charges for each student ticket = $7

Charges for each adult ticket = $12

Let number of children tickets =
`2x`

Ticket price for children =
`\$ 2x * 5`

As per question statement, there were half as many adults as there are children,

so number of adult tickets =
`x`

Ticket price for adults =
`\$ x * 12`

Now, number of students =

`(271-x-2x)\\\Rightarrow (271-3x)`

Ticket price for students =
`\$ (271-3x) * 7`

Total ticket sales = $1974

`\Rightarrow 12x+2x* 5 +(271-3x)* 7 = 1974\\\Rightarrow 22x-21x +(271 * 7) = 1974\\\Rightarrow x = 1974 - 1897\\\Rightarrow x = 77`

So, number of adults attended = 77

number of children attended = 77
`*` 2 = 154

number of students attended = 271 - 77 - 154 = 40