Question 587861: A Broadway theater has 400 seats, divided into orchestra, main and balcony seating. Orchestra seats sell for $80, main seats for $60 and balcony seats for $40. If all the seats are sold, the gross revenue to the theater is $23,200. If all the main seats and the balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $20,000. How many are there of each seat?
I've tried solving this by writing an equation and trying to solve for x but it didn't get me the correct answer, any help would be appreciated. Thank you.
Found 2 solutions by mananth, yogendra singh:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! A Broadway theater has 400 seats,
orchestra,(x) main (y)and balcony seating(z)
x+y +z= 400.........................(1)
Orchestra seats sell for $80, main seats for $60 and balcony seats for $40. If all the seats are sold, the gross revenue to the theater is $23,200.
80x+60y+40z=23200...................(2)
If all the main seats and the balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $20,000.
60y++40z+(x/2) *80 = 20,000
40x+60y+80z=20,000.................(3)
80x+60y+40z=23200...................(2)
rewrite this equation
40x+(40x+60y+40z)= 23200
But
40x+60y+80z=20,000
so 40x+20000=23200
40x=23200-20000
40x = 3200
/40
x= 80 seats that of Orchestra.
consider equation (1) & (2)
x+y+z=400
80+y+z=400
y+z=400-80
y+z=320.....................(4)
80x+60y+40z=23200
80*80 +60y+40z=23200
60y+40z= 23200-6400
60y+40z=16800
divide by 20
3y+2z=840...................(5)
solve equations (4) & (5)
y+z=320
3y+2z=840
multiply (4) by -2 and it to (5)
-2y-2z=-640
Add up
y= 200
Now x= 80, y =200 so z= 120
Check
6400+12000+4800= 23200
Answer by yogendra singh(2)  (Show Source):
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