equations solve

Question

A theater has a seating capacity of 1050 and charges $0.85 for children, $3.35 for students, and $4.30 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The total money brought in was $3180. How many children, students, and adults attended the show?

Answer 1

A=(C+S)/2

.85C + 3.35S + 4.3A = 3180

.85 C + 3.35S +4.3(C+S)/2 = 3180

.85C + 2.15C + 3.35S + 2.15S = 3180

3C + 5.5S = 3180

C+S+A = 1050

C+S + (S+C)/2 = 1050

C+S + S/2 + C/2 = 1050

3C/2 + 3S/2 = 1050

C + S = 1050(2/3) = 2(350) = 700

3C +3S = 2100 subtract that from 3C+5.5S = 3180

2.5S = 1080

S = 1080/2.5 = 432 students

C+S = 700

C = 700-432 = 268 children

A = (1/2)() = (432+268) = 700/2 =350 adults

432+268+350 = 1050

.85(268) + 3.35(432) + 4.3(350) = 3180

answer is" 268 children, 432 students, and 350 adults