A string is cut into two parts.The ratio of lengths of the string and the smaller part is six times the ratio of lengths of the smaller and the larger parts .Find the ratio of the lenghths of the larger and the smaller parts of the string.

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  1. let the string be 1 unit of length
    shorter piece --- x
    longer piece ---- 1-x

    ratio of string to smaller part = 1/x
    ratio of smaller part to larger part = x/(1-x)

    1/x = 6(x/(1-x)
    1/x = 6x/(1-x)
    6x^1 = 1 - x
    6x^2 + x - 1 = 0
    (3x - 1)(2x + 1) = 0
    x = 1/3 or x = -1/2, the last answer makes no sense

    so smaller is 1/3, larger is 2/3
    ratio of larger to smaller
    = (2/3) / (1/3)
    = 2 : 1

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