A broadway theatre has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $40, main seats for $25, and balcony seats for $20. If all the seats are sold, the gross revenue to the theatre is $13,150. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $11,150. How many are there of each kind of seat?

How many are there of each kind of seat?

orchestra 100, main 230, and balcony 170

Step-by-step explanation:

x = Orchestra seats

y = Main seats

z = Balcony seats

x + y + z = 500

:

If all the seats are sold, the gross revenue to the theatre is $13,150."

40x + 25y + 20z = 13150

:

"but if only half the orchestra seats are sold, the gross revenue is $11,150."

(40:2) x) + 25y + 20z = 11150

20x + 25y + 20z = 11150

use elimination on these two equations

40x + 25y + 20z = 13150

20x + 25y + 20z = 11150

20x = 2000

x = 2000:20

x = 100 orchestra seats

100 + y + z = 500

y + z = 500 - 100

y + z = 400

25y + 20z = 9150

20y + 20z = 8000

5y = 1150

y = 1150:5

y = 230 Main seats

100 + 230 + z = 500

z = 500 - 330

z = 170 Balcony seats