Question

A movie theater sells tickets at different prices. Adults are charged $8.50 per ticket, and children are charged $5.50 per ticket. If the theater sells 26 tickets for $194, how many adult tickets and how many child tickets were sold?

Answer 1

9 child tickets and 17 adult tickets were sold.

Explanation:

Let the number of adult tickets sold be
`a`

and the number of child tickets be
`c`.

The theater sold a total number of 26 tickets.

This means that:
`a+c=26`.....eqn1

The theater made a total sale od $194.

This implies that:

`8.5a+5.5c=194`...eqn2

We make
`a` the subject in equation 1:
`a=26-c`...eqn3

Substitute equation (3) into equation (2)

`8.5(26-c)+5.5c=194`

Expand to get:
`221-8.5c+5.5c=194`

`-8.5c+5.5c=194-221`

`-8.5c+5.5c=194-221`

`-3c=-27`

`\implies c=9`

Put c=9 into equation (3) to get:
`a=26-9=17`

Therefore 9 child tickets and 17 adult tickets were sold.