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20 February, 11:41

University Theater sold 556 tickets for a play. Tickets cost $22 per adultand $12 per senior citizen. If total receipts were $8492, how many seniorcitizen tickets were sold?

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  1. 20 February, 13:48
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    To find the answer, set up a system of equations.

    Let x=adult tickets and y=senior citizen tickets.

    x+y=556

    22x+12y=8492

    Change the first equation to make it easy to combine with the second equation.

    y=556-x

    Now substitute (556-x) for y in the second equation.

    22x+12 (556-x) = 8492

    Simplify and combine like terms.

    22x+6672-12x=8492

    10x=1820

    x=182

    182 adult tickets were sold, so to solve for the number of senior citizen tickets sold, subtract 182 from 556.

    556-182=374

    374 senior citizen tickets were sold.
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