SOLUTION: An amateur drama group hire a theatre for their production. They expect to sell all 850 tickets, some at $12 and the rest at $8. The group require the ticket sales to cover their $

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Question 424756: An amateur drama group hire a theatre for their production. They expect to sell all 850 tickets, some at $12 and the rest at $8. The group require the ticket sales to cover their $3760 production costs and to make a profit of $4000. If they are to exactly achieve this target and their expectations regarding ticket sales are correct how many of the 850 tickets should they charge $12 for and how many should they charge $8 for?
(Need help thanks!!)
Found 2 solutions by htmentor, stanbon:
Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website!
Let x = the number of $8 tickets.
Then 850-x = the number of $12 tickets.
Setting up the problem in equation form, we have
8x + 12(850-x) = 3760 + 4000
Collect terms and solve for x:
-4x + 10200 = 7760 -> x = 610
So they need to sell 610 $8 tickets and 850 - 610 = 240 $12 tickets

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
They expect to sell all 850 tickets, some at $12 and the rest at $8.
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Quantity Eq: t + e = 850 tickets
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The group require the ticket sales to cover their $3760 production costs and to make a profit of $4000.
Value Equation: 12t + 8e = 7760 dollars
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If they are to exactly achieve this target and their expectations regarding ticket sales are correct how many of the 850 tickets should they charge $12 for and how many should they charge $8 for?
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Multiply thru the Quantity Eq. by 12:
12t + 12e = 12*850
12t + 8e = 7760
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Subtract to get:
4e = 2440
e = 610 (# of $8 tickets needed)
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Solve for "t":
t + e = 850
t + 610 = 850
t = 240 (# of $12 tickets needed)
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Cheers,
Stan H.