college algebra

Question

A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $140, main seats for $115, and balcony seats for $100. If all the

seats are full, the gross revenue of the theater is $57,300. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $50,300.

How many of each kind of seat are there?

Answer 1

o + m + b = 500

140o + 115m + 100b = 57300

140o + 115m + 100b/2 = 50300

100b/2 = 50b, so if I subtract equation #3 from #2, I get...

50b = 7000

b = 140 balcony seats

Keep playing with it to figure out the rest. You got this!