AMC 12 Mock Exam 3 Problem 1

Problem 1 of 25

A community theater charges $\$12$ for an adult ticket and $\$7$ for a child ticket. For Saturday's matinee it sold $50$ more child tickets than adult tickets, and its ticket revenue for the matinee was $\$1490$ . How many tickets in all did the theater sell for the matinee?

Show solution

Solution

Let $a$ be the number of adult tickets, so $a+50$ child tickets were sold. Then $12a+7(a+50)=1490$ , so $19a=1140$ and $a=60$ . The total is $a+(a+50)=60+110=\boxed{170}$ .

Tagged: linear equation from a ticket-sales story

Answer choices

Solution