A question about systems of equations

Question

A movie theater has a seating capacity of 367. The theater charges $5 for children, $7 for students, and $12 of adults. There are half as many adults as there are children. If the total ticket sales was $2,658, How many children, students, and adults attended?

Im not sure how to do this

Answer 1

C+S+A = 367, A=C/2

5C+7S + 12A = 2658

7C + 7S + 7A = 7(367) = 2569

7C+7S + 7A = 2569

5C +7S +12A =2658

-2C + 5A = 89

-2C +5(C/2) = 89

C/2 = 89 adults

C = 178 children

S= 367-178-89 = 100 students