Question 1154614: A Broadway theater has 400 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 70 comma main seats for $ 60 comma and balcony seats for $ 35. If all the seats are sold, the gross revenue to the theater is $ 21 comma 300. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 18 comma 500. How many are there of each kind of seat?
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! The description would be best based on this:
Theater has 400 seats.
Orchestra Seats, $70 each;
Main Seats, $60 each;
Balcony Seats, $35 each;
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Gross Revenue, $21300;
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If ALL the Main and Balcony seats sold and only HALF the Orchestra seats sold, Gross Revenue would be $18500.
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r, Orchestra seats
m, Main seats
b, Balcony seats
Look at the first two equations, and see that both of them contain the expression,  . The value for r should be found very quickly because the description and resulting equations allows two variables to be easily eliminated. Otherwise, solution methods may vary.
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