Question

A movie theater has a seating capacity of 253. 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 $ 1828 on a sold out night, how many children, students, and adults attended?

children attended=
adults attended=
students attended=

Answer 1

children attended= 114

adults attended= 57

students attended= 82

Explanation:

children attended= c

adults attended= a

students attended= s

c+s+a = 253

5c + 7s + 12a = 1828

c=2a

2a + s + a =253

5*2a + 7s + 12a = 1828

3a + s = 253

22a + 7s = 1828

s = 253 - 3a

22a + 7(253 - 3a) = 1828

22a - 21a + 7*253 = 1828

a = 1828 - 7*253

a = 57

s = 253 - 3a = 253 - 3*57 = 82

s = 82

c=2a=2*57= 114

c=114