Pre-Calculus, 9th edition
75

 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 .

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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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