SOLUTION: The manager of a movie theater found that Saturday's sales were $3675. He knew that a total of 650 tickets were sold Saturday. Adult tickets cost $7.50 and children's tickets cos

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Question 279151: The manager of a movie theater found that Saturday's sales were $3675. He knew that a total of 650 tickets were sold Saturday. Adult tickets cost $7.50 and children's tickets cost $4.50. Write equations to represent the number of tickets sold and the amount of money collected. How many of each kind of ticket were sold?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The manager of a movie theater found that Saturday's sales were $3675. He knew that a total of 650 tickets were sold Saturday. Adult tickets cost $7.50 and children's tickets cost $4.50. Write equations to represent the number of tickets sold and the amount of money collected. How many of each kind of ticket were sold?
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Equations:
Quantity Eq:::: a + c = 650
Value Equation:7.5a + 4.5c = 3675
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Multiply thru 1st equation by 75:
Multiply thru 2nd equation by 10:
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75a + 75c = 75*650
75a + 45c = 36750
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Subtract 2nd from 1st and solve for "c":
30c = 12000
c = 400 (# of children's tickets sold)
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Since a+c = 650
a = 250 (# of adult tickets sold)
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Cheers,
Stan H.