Algebra 2

At a county fair, adults' tickets sold for $5.50, senior citizens' tickets for $4.00, and children's tickets for $1.50. On the opening day, the number of children's and senior's tickets sold was 30 more than half of the number of adults' tickets sold. the number senior citizens' tickets sold was 5 more than four times the number of children's tickets. How many of each type of ticket were sold if the total receipts from the ticket sales were $14, 970?

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  1. X = The # of adult tickets sold.

    X/2 + 30 = The # of seniors & children
    tickets sold.

    5.5x + 5.5(x/2+30) = $14,970,
    5.5x + 2.75x + 165 = 14,970,
    8.25x + 165 = 14,970,
    8.25x = 14,970 - 165 = 14,805,
    X = 1795 Adult tickets sold.

    x/2 + 30 = 1795/2 + 30 = 928 Children's
    and seniors tickets sold.

    Y = The # of children's tickets sold.
    4y + 5 = The # of senior's tickets sold.

    y + (4y+5) = 928,
    5y + 5 = 928,
    5y = 928 - 5 = 923,
    Y = 185 Children's tickets sold.

    4y + 5 = 4*185 + 5 = 745 Senior tickets

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