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The denominator of a fraction is three more than twice the numerator. If both numerator and denominator are decreased by seven, the simplified result is 7 divided by19. Find the original fraction. (Do NOT simplify.)

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3 answers
  1. In original fraction:
    numerator ---- x
    denominator ---- 2x+3
    so the fraction was x/(2x+3)

    after change:
    fraction is (x-7)/(2x+3 - 7) = 7/19
    (x-7)/(2x-4) = 7/19
    19x - 133 = 14x - 28
    5x = 105
    x = 21

    the original fraction is 21/45

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    Reiny
  2. original fraction: n/(n+3)
    (n-7)/(n+3-7) = 7/19
    So solve for n

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    oobleck
  3. my bad. I missed the "twice"

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    oobleck

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