A movie theater has a seating capacity of 273.

Question

A movie theater has a seating capacity of 273. 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 $ 1988, How many children, students, and adults attended?

   children attended.

   students attended.

   adults attended.

Answer 1

5C+7S+12A = 1988

C+S+A =273

A=C/2

C=2A

7C+7S+7A=7(273)=1911

subtract last equation from 1st

-2C+5A = 77

substitute 2A for C

-2(2A)+5A = 77

-4A +5A=77

A=77

C=2A=2(77) =154

S=273-77-154=44

154 Children, 44 Students, 77 Adults