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Let $\"\"$ be number of orchsetra seats which costs $\"\"$ .

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Let $\"\"$ be the number of main seats which costs $\"\"$ .

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Let $\"\"$ be the number of balcony seats which costs $\"\"$ .

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Since total number of seats is $\"\"$ , $\"\"$ .

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Since the total revenue is $\"\"$ if all seats are sold , $\"\"$ .

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If only half of the orchestra seats are sold the revenue is $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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From the data , the system of equations are $\"\"$ .

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Multiple to each side the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$ .

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$\"\"$

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Multiple to each side the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$ .

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$\"\"$

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Substiute $\"\"$ in equation $\"\"$ .

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$\"\"$

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Substiute $\"\"$ and $\"\"$ in equation $\"\"$ .

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$\"\"$

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The solution is $\"\"$ and $\"\"$ .

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Therefore there are $\"\"$ orchsetra seats, $\"\"$ main seats and $\"\"$ balcony seats.

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Number of orchsetra seats are $\"\"$ .

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Number of main seats are $\"\"$ .

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Number of balcony seats are $\"\"$ .