SOLUTION: A theater has a seating capacity of 600 and charges $3 for children, $5 for students, and $7 for adults. At a certain screening with full attendance, there were half as many adults
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Question 514480: A theater has a seating capacity of 600 and charges $3 for children, $5 for students, and $7 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $3200. How many children attended the show? (Let x, y, and z denote the number of children, students, and adults, respectively.)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Like the man said, let 
represent the number of children, let 
represent the number of students, and let 
represent the number of adults.
The first thing I did was represent the number of adults in terms of the combined number of children and students.
But since we know that there were 600 in attendance, we can say:
Substituting:
A little algebra music:
and therefore
Furthermore:
Now we write a value equation:
And then substitute what we know about and :
\ +\ 7(200)\ =\ 3200)
All that is left is to solve for , the number of children.
John
My calculator said it, I believe it, that settles it
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