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| PAGE: 711 | SET: Exercises | PROBLEM: 75 |
Let 
be number of orchsetra seats which costs 
.
Let 
be the number of main seats which costs 
.
Let 
be the number of balcony seats which costs 
.
Since total number of seats is 
, 
.
Since the total revenue is 
if all seats are sold ,
.
If only half of the orchestra seats are sold the revenue is 
.
.
.
From the data , the system of equations are 
.
Multiple to each side the equation 
by 
and add to the equation 
to eliminate 
.
.
Multiple to each side the equation 
by 
and add to the equation to eliminate .
.
Substiute 
in equation 
.
Substiute 
and 
in equation .
The solution is 
and 
.
Therefore there are 
orchsetra seats, 
main seats and 
balcony seats.
Number of orchsetra seats are 
.
Number of main seats are 
.
Number of balcony seats are 
.
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