college algebra word problem

Question

A local band sells out for their concert. They sell all 1,155 tickets for a total purse of $28,122.50. The tickets were priced at $20 for student tickets, $22.50 for children, and $29 for adult tickets. If the band sold twice as many adult as children tickets, how many of each type was sold?

Answer 1

20S+ 22.5C + 29A = 28122.5

2C=A

S+C+A = 1155

S+C+2C = 1155

S+3C = 1155

S=1155-3C

A=C/2

20(1155-3C) + 22.5C + 29(C/2) = 28122.5

expand, isolate C and solve for C

then A = double that

while S = 1155-3C