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?

Accepted Solution

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].....eqn1The theater made a total sale od $194.This implies that:[tex]8.5a+5.5c=194[/tex]...eqn2We make [tex]a[/tex] the subject in equation 1: [tex]a=26-c[/tex]...eqn3Substitute 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.