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?
Accepted Solution
A:
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