math

Julia had 150 fewer bonus points than Kelly.Bothgirls used tthe same number of bonus points. Julia was left with 1 out of 2 of her bonus pointand Kelly was left with 3 out of 4 of her bonus points.how many bonus did Kelly have at first

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  1. Kelly's original number of bonus point --- x
    Julia's original number of bonus points -- x-150

    let the number used by both be y each.

    now Kelly has x - y
    Julia has x-150 - y

    for Kelly:
    (x-y)/x = 3/4
    4x - 4y = 3x
    x - 4y = 0 or x = 4y

    for Julia:
    (x-150-y)/(x-150) = 1/2
    2x - 300 - 2y = x- 150
    x - 2y = 150

    but x = 4y
    4y - 2y = 150
    y = 75
    then x = 4(75) = 300

    so originally,
    Kelly had 300 and Julia had 150


    check:
    so they each used up 75
    leaving Kelly with 225 and Julia with 75

    Does Julia have 1/2 or her original ? YES
    Does Kelly have 3/4 of her original ? YES

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