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A Broadway theater has 600 seats, divided into orchestra, main, and balcony seating.
Orchestra seats sell for $60 main seats for $50 and balcony seats for $30.
If all the seats are sold, the gross revenue to the theater is $27,000
If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $23,400
How many are there of each kind of seat?
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From the condition, half the orchestra seats cost 27000 - 23400 = 3600 dollars.
Thus the half the number of orchestra seats is = 60,
and full number of orchestra seats is 2*60 = 120.
Part of the problem is just solved.
For the other part, we have
- the cost of main and balcony seats total of 23400-3600 = 19800 dollars, and
- the total of these two types of seats is 600-120 = 480.
Let x be the number of main seats; then the number of the balcony seats is (480-x).
Then we write the money equation for these two types of seats
50*x + 30*(480-x) = 19800 dollars.
From this equation x = = 270.
ANSWER. 120 orchestra seats; 270 main seats and the rest 600-120-270 = 210 seats.
Solved.