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Question

A broadway theater has 400 seats, divided into orchestra, main, and balcony seating. ... a broadway theater has 400 seats, divided into orchestra, main, and balcony seating. orchestra seats sell for $50, main seats for $30 and balcony for $25. If all seats are sold, the gross revenue to the theater is $13,000. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $11,000. How many are there of each kind?

Answer 1

O = orchestra seats at $50

M = main seats at $30

B = balcony seats at $25

400 seats, so (1) O + M + B = 400

(2) 50 O + 30 M + 25 B = 13000

(3) 1/2 (50 O) + 30 M + 25 B = 11000

Subtract equation 3 from equation 2

1/2(50 O) = 13000 - 11000

25O = 2000

O = 80

Subtract from (1)

M + B = 320

Subtract 25O = 2000 from (3)

30M + 25 B = 9000

25M + 25B = (320)(25) = 8000

Subtracting, 5M = 1000

M = 200

B = 320 - M

B = 120