Question 523626
A theater has a seating capacity of 732 and charges $4 for children, $6 for students, and $8 for adults.
 At a certain screening with full attendance, there were half as many adults as children and students combined.
 The receipts totaled $4540. How many children attended the show?
:
Let c = no. of children
Let s = no. of students
Let a = no. of adults
:
Write an equation for each statement:
:
"A theater has a seating capacity of 732"
c + s + a = 732
:
"charges $4 for children, $6 for students, and $8 for adults.  The receipts totaled $4540"
4c + 6s + 8a = 4540
:
"there were half as many adults as children and students combined."
a = .5(c+s)
:
In the 1st equation, replace a with .5(c+s)
c + s + .5(c+s) = 732
c + s + .5c + .5s = 732
1.5c + 1.5s = 732
:
Do the same in the 2nd equation
4c + 6s + 8(.5(c+s)) = 4540
4c + 6s + 4c + 4s = 4540
8c + 10s = 4540
:
Multiply the 1st equation by 20, the above equation by 3
30c + 30s = 14640
24c + 30s = 13620
-------------------subtraction eliminates s, find c:
6c = 1020
c = {{{1020/6}}}
c = 170 children went to the performance