system of linear

Question

A movie theater has a seating capacity of 163. 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 $ 1172, How many children, students, and adults attended?

    children attended.

    students attended.

    adults attended.

Answer 1

c+s+a =163

7c+7s+7a= 1141

a=c/2

c=2a

5c+7s+12a = 1172

subtract 2nd from 5th equation

-2c+5a =31

-2(2a)+5a =31

a=31 adults

c=62 children

s =163-93= 70 students

5(62)+7(70)+12(31

= 310+490+372=1172