A movie theater has a seating capacity of 295. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. If the total ticket sales was $ 2144

Question

A movie theater has a seating capacity of 295. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2144, How many children, students, and adults attended?

Answer 1

158 children, 58 students, 79 adults

C,S,A = children, students, adults (not Confederate States of America, for any Civil War buffs out there)

C + S + A = 295

C = 2A

5C + 7S + 12A = 2144

3 equations, 3 unknowns, solve by substitution and eliminaton or maybe by matrix algebra

5(158) + 7(58) + 12(79) = 790 + 406 + 948 = 2144