Math

If the numerator of a fractionis multiplied by 4 and the denominatoris reduced by 2,the result is 2.if the numerator of the fraction is increase by 15 and 2 subtracted from the double of the denominator the result is 9/7, find the fraction.plz tell me step by step

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  1. done. see related questions below.

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  2. OK, let's see whether I can clarify it a bit.

    If the original fraction is n/d, then we are told:

    numerator of a fraction is multiplied by 4: change n to 4n
    denominator is reduced by 2: change d to d-2

    4n/(d-2) = 2

    Similar changes for the 2nd half, giving us
    (n+15)/(2d-2) = 9/7

    Now just find n and d:

    4n/(d-2) = 2
    (n+15)/(2d-2) = 9/7

    4n = 2(d-2)
    7(n+15) = 9(2d-2)

    4n = 2d-4
    7n + 105 = 18d - 18

    4n-2d = -4
    7n-18d = -123

    36n-18d = -36
    7n-18d = -123

    29n = 87
    n=3

    Now use that in 4n-2d = -4 to get
    d = 8

    So the original fraction is 3/8

    check:

    4*3/(8-2) = 12/6 = 2
    (3+15)/(2*8-2) = 18/14 = 9/7

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