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Let $\"\"$ be number of adult tickets which costs $\"\"$ .

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Let $\"\"$ be the number of child tickets which costs $\"\"$ .

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Let $\"\"$ be the number of senior citizen tickets 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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Twice as many children’s tickets were sold as adult tickets, therefore $\"\"$ .

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

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

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$\"\"$

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Substiute the value $\"\"$ in equation $\"\"$ .

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

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$\"\"$

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

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Therefore there are $\"\"$ adults, $\"\"$ children and $\"\"$ senior citizens went to theater that day.

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There are $\"\"$ adults, $\"\"$ children and $\"\"$ senior citizens went to theater that day. \ \