college algebra

Question

A movie theater has a seating capacity of 341. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2482, How many children, students, and adults attended?

Answer 1

5C+7S+12A =2482

A=C/2

5C+7S+6C = 2482

11C +7S = 2482

C+S+A = 341

S=341-C-C/2 = 341-3C/2

11C+7(341)-21C/2 = 2482

C/2 = 2482- 2387 = 95

C = 2(95)= 190 children

A = 190/2 = 95 adults

S = 341-190-95 = 56 students

5(190) + 7(56) + 12(95) = 392 + 22(95) = 392 + 2090 = 2482