How many children,students,and adults attended?

Question

A movie theater has a seating capacity of 367. The theater charges $5.00 for children, $7.00 forstudents, and $12.00 of adults. There are half as many adults as there are children. If the total ticket

sales was $2660 on a sold out night, how many children, students, and adults attended?

Answer 1

c+s+a = 367

a=c/2

5c+7s+12a = 2660

5c+5s+5a = 5(367)= 1835

subtract

2s +7a = 2660-1835 = 825

2s +7(c/2) = 2s +7c/2 = 825

4s +7c = 1650

c+s+c/2 = 367

2c+2s+c =734

2s +3c =734

4s+6c=1468

4s+7c =1650

c = 182 children

a= 91 adults

s = 367-273 = 94 students

5(182)+7(94)+12(91)

= 910+658+1092

=2660