Question 404777: A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z). At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $3080. How many children attended the show?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z).
At a certain screening with full attendance, there were half as many adults as children and students combined.
The receipts totaled $3080.
How many children attended the show?
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Equations:
People: x + y + z = 720
Quantity: z = (1/2)(x+y)
Values: 2x + 4y + 6z = 3080
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Rearrange:
x + y + z = 720
x + y -2z = 0
x +2y +3z = 1540
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Use whatever method you know to get:
x = 140
y = 340
z = 240
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Cheers,
Stan H.
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