SOLUTION: a broadway theatre has 500 seats,divided onto orchestra,main,and balcony seating.orchestra seats sell for $50,main seats for $35 and balcony for $25. if all the seats are sold the

Question 356210: a broadway theatre has 500 seats,divided onto orchestra,main,and balcony seating.orchestra seats sell for $50,main seats for $35 and balcony for $25. if all the seats are sold the gross revenue to the theater is $17100. if all the main and balcony seats are sold, but only half the orchestra seats are sold the gross revenue is $14600. how many are there of each kind of seat?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let orchestra seats be x $50
main seats be y $35
and balcony seats be z $25
...
x+y+z=500--------------1
50x+35y+25z= 17100 -----2
25x+35y +25z = 14600------3
subtract 3 from 2
25x=3000
x= 3000/25
x= 120 seats--- orchestra seats
...
multiply 1 by 25
25*120+25y+25z=12500
25y+25z=12500-3000
25y+25z=9500.................4
...
equation2 = 6000+35y+25z=17100
35y+25z=11100.................5
...
subtract 4 from 5
10y=1600
y=160 main seats
...
z you can calculate 160+120=280
500 -280= 220 balcony seats
...
m.ananth@hotmail.ca
..

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