SOLUTION: A local civic arena is negotiating a contract with a touring ice-skating show, Icey Blades. Icey Blades charges a flat fee of $60,000 per night plus 40 percent of the gate receipts

Question 1136049: A local civic arena is negotiating a contract with a touring ice-skating show, Icey Blades. Icey Blades charges a flat fee of $60,000 per night plus 40 percent of the gate receipts. The civic arena plans to change one price for all seats, $12.50 per ticket.
(a)Determine the number of tickets which must be sold each night in order to break even.
(b)if the civic arena has a goal of clearing $15000 each night, how many tickets must be sold?
(c)what should nightly profit equal if average attendance is 7500 per night?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
(a)Determine the number of tickets which must be sold each night in order to break even.

12.50x = 0.40(12.50x) + 60000

12.50x = 5x + 60000

7.50x = 60000

x = 8000

(b)if the civic arena has a goal of clearing $15000 each night, how many tickets must be sold?

12.50x = (0.40(12.50x) + 60000) + 15000

12.50x = 5x + 75000

7.50x = 75000

x = 10000

(c)what should nightly profit equal if average attendance is 7500 per night?

x = 12.50(7500) - (0.40(12.50)(7500) + 60000)

x = 12.50(7500) - 0.40(12.50)(7500) - 60000

x = 93750 - 37500 - 60000

x = -3750

If the attendance averages 7500 per night, there will be a LOSS of $3750 per night.
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