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Math

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Andrea sells tickets at the Showtime Cinema. On Thursday night, Back to the Future was playing. Adults, senior citizens and children bought tickets at the following rates:

Adults $5.00
Senior Citizens $1.00
Children $.10

Andrea sold 100 tickets worth $100. How many adult, senior and children tickets were sold?

  • Math -

    number of adults --- x
    number of seniors --- y
    number of children 100-x-y

    5x + y + .1(100-x-x-y) = 100
    times 10
    50x + 10y + 100 -x-y = 1000
    49x + 9y = 900

    We are looking for integer solutions of x and y, (can't have partial people)

    the x-intercept is appr 19
    the y-intercept is appr 90

    49x = 900-9y
    x = (900-9y)/49

    so 900-9y must be a multiple of 49

    starting with trials of y = 1, 2, 3, ..
    I lucked out at y = 2
    when y = 2
    x = 18

    knowing the slope of our linear equation is -49/9
    increasing the y value by 49 and decreasing the x by 9 would give us another solution.
    so y = 51 and x = 9 would be another solution

    so case 1:
    18 adults
    2 seniors
    80 children
    check:
    -- sum is 100,
    -- income = 5(18) + 1(2) + .1(80) = $100

    case 2:
    9 adults
    51 seniors
    40 children

    check:
    --- sum is 100
    -- income = 5(9) + 1(51) + .1(40) = 100

    (there is a third case of
    0 adults
    100 students
    0 children , but it said that adults, seniors and children bought tickets , so I would exclude that)

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