Answer:
9 child tickets and 17 adult tickets were sold.
Step-by-step explanation:
Let the number of adult tickets sold be [tex]a[/tex]
and the number of child tickets be [tex]c[/tex].
The theater sold a total number of 26 tickets.
This means that: [tex]a+c=26[/tex].....eqn1
The theater made a total sale od $194.
This implies that:
[tex]8.5a+5.5c=194[/tex]...eqn2
We make [tex]a[/tex] the subject in equation 1: [tex]a=26-c[/tex]...eqn3
Substitute equation (3) into equation (2)
[tex]8.5(26-c)+5.5c=194[/tex]
Expand to get: [tex]221-8.5c+5.5c=194[/tex]
[tex]-8.5c+5.5c=194-221[/tex]
[tex]-8.5c+5.5c=194-221[/tex]
[tex]-3c=-27[/tex]
[tex]\implies c=9[/tex]
Put c=9 into equation (3) to get:[tex]a=26-9=17[/tex]
Therefore 9 child tickets and 17 adult tickets were sold.
