Linear Question

Question

A movie theater has a seating capacity of 289. 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 $ 2106, How many children, students, and adults attended?

Answer 1

C= 2A

C+S+A = 289

5C + 7S + 12A = 2106

7C + 7S + 7A = 7(289) = 2023, subtract to get

-2C +5A = 83

-2(2A) + 5A = 83

A = 83 adults

C = 2A = 2(83) = 166 children

S = 289-C-A = 289-83-166 = 289-249 = 40 students