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) About Me  (Show Source):
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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 :



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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