SOLUTION: A theater has a seating capacity of 753 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

Question 495754: A theater has a seating capacity of 753 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 $4051. How many children attended the show?

So here's what I have...
x= children, $3
y= students, $5
z= adults, $7
x + y + z = 753
3x + 5y + 7z = 4051
now all i need is a third equation that represents "there were half as many adults as children and students combined"
I was thinking maybe it would be x + y = .5z
so then to get all the variables on the left side would it be x + y -.5z = 0
I can solve the equation once I have all three equations, with the variables all to one side of the equals sign, but i'm not sure how to write the equation.
Also, how would I write the equation for "x is to be twice the sum of y and z"
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use x + y -.5z = 0 as your 3rd equation.
Cheers,
Stan H.
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