Question 1110078: Suppose that a theater sells matinee tickets for $7.00, while normal tickets are $12.50, and 3D tickets are $18.00. On a certain day, 8,526 people visited the theater and twice as many people bought matinee tickets or normal tickets as those who bought 3D tickets. A total of $105,304.50 in ticket sales was collected. Determine how many of each type of ticket was sold.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that a theater sells matinee tickets for $7.00, while normal tickets are $12.50, and 3D tickets are $18.00. On a certain day, 8,526 people visited the theater and twice as many people bought matinee tickets or normal tickets as those who bought 3D tickets. A total of $105,304.50 in ticket sales was collected. Determine how many of each type of ticket was sold.
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Equations:
Value Eq:: 7m + 12.5n + 18D = 105,304.50 dollars
Quantity Eq:: m + n + D = 8526
Quantity Eq:: m+n = 2D
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Substitute::
2D+D = 8526
D = 2842
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7m + 12.5n = 105,304.5-18*2842
m + n = 8526-2842
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7m + 12.5n = 54148.5
7m + 7n = 7*5684
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5.5n = 14360.5
n = 2611 tickets
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m = 8526-2842-2611 = 3073
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Cheers,
Stan H.
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