Problema Solution
A theatre has 500 seats, divided into orchestra, main, and balcony. Seats sell for $80 Orchestra, $70 main, and $40 balcony. If all seats are sold, the gross revenue to the theatre is $31,500. If all the main and balcony seats are sold, and half of the orchestra seats, the gross revenue is $27,500. How many are there of each kind of seat?
Answer provided by our tutors
The total number of seats=500
Let the number of seats in Orchestra=x.
Number of seats in mail=y
Number of seats in Balcony=z.
Then from the given information 80x+70y+40z=31500
=> 70y+40z=31500-80x
and 40x+70y+40z=27500
=>70y+40z=27500-40x
So 31500-80x=27500-40x
=> x=4000/40
x=100
=> y+z=500-100
=> y+z=400
70y+40z=27500-40x
=>30y+40(y+z)=27500-40(100)
=> y=27500-4000-40(400)
=>y=250
=> z=150
So the number of seats in orchestra=100
Number of seats in main=250
Number of seats in Balcony=150