Question

A Broadway theater has 500 seats, dividing into orchestra, main, and balcony seating. Orchestra seats sell for $50, main seats for $40, and balcony seats for $25. If all the seats are sold, the gross revenue to the theater is $18,600. If all the main and balcony seats are sold but only half the orchestra seats are sold, the gross revenue is $16,100. How many are there of each kind of seat?

Answer 1

Let there are x orchestra seats, y main seats and z balcony seats.

Now, since total number of seats is 500, so we have,

x + y + z = 500............. (1)

Again according to selling price of each seat, we have,

50x + 40y + 25z = 18600.............(2)

and, 50*(x/2) + 40y + 25z = 16100

i.e. 25x + 40y + 25z = 16100............(3)

Now (2) - (3) gives,

50x - 25x = 18600 - 16100

i.e. 25x = 2500

i.e. x = 100

So, from (1) we get, y + z = 400..........(4)

And from (3), 40y + 25z = 13600.........(5)

Now (5) - 25*(4) gives,

40y - 25y = 13600 - 10000

i.e. 15y = 3600

i.e. y = 240

So from (4), z = 400 - 240 = 160

So there are 100 orchestra seats, 240 main seats and 160 balcony seats.