Question 424756
 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.