SOLUTION: A Broadway theater has 600 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $70, main seats for $60, and balcony seats for $35. If all the seats a

Question 441195: A Broadway theater has 600 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $70, main seats for $60, and balcony seats for $35. If all the seats are sold, the gross revenue to the theater is $32,950. If all the main and balcony seats are sold, but only have the orchestra seats are sold, the gross revenue is $28,750. How many are there of each kind of seat?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let b = the number of balcony seats sold
Let m = the number of main seats sold
Then 600 - b - m = the number of orchestra seats sold
For the gross revenue we can write
35b + 60m + 70(600 - b - m) = 32950
If only half the orchestra seats are sold we can write
35b + 60m + 70(600 - b - m)/2 = 28750
Simplifying gives:
35b + 60m + 42000 - 70b - 70m = 32950
35b + 10m = 9050 [1]
35b + 60m + 21000 - 35b - 35m = 28750
25m = 7750 -> m = 310
Substituting this value for m into [1] gives
35b + 3100 = 9050 -> b = 170
So the number of orchestra seats sold is 600 - 170 - 310 = 120
Ans: Balcony seats = 170; Main seats = 310; Orchestra seats = 120

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