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

Answer:

9 child tickets and 17 adult tickets were sold.

Step-by-step 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.