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?

Answer: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 = 1115020x = 2000 x = 2000÷20 x = 100 orchestra seats100 + y + z = 500 y + z = 500 - 100 y + z = 40025y + 20z = 9150 20y + 20z = 80005y = 1150 y = 1150÷5 y = 230 Main seats 100 + 230 + z = 500 z = 500 - 330 z = 170 Balcony seats