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Math Help - word problem

  1. #1
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    word problem

    The denominator of a fraction is 3 less than twice the numerator.If the numerator were doubled and the denominator increased by 8, the resulting fraction would be 2/3.Find the original fraction.
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  2. #2
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    Quote Originally Posted by Panaboy
    The denominator of a fraction is 3 less than twice the numerator.If the numerator were doubled and the denominator increased by 8, the resulting fraction would be 2/3.Find the original fraction.
    Let n = numerator
    And d = denominator

    d = 2n -3 ------(i)
    2n / (d+8) = 2/3 -------(ii)

    Substitute the d from (i) into (ii),
    2n / (2n-3 +8) = 2/3
    2n / (2n +5) = 2/3
    Cross multiply,
    2n(3) = (2n +5)(2)
    6n = 4n +10
    6n -4n = 10
    2n = 10
    n = 10/2 = 5 --------***
    So,
    d = 2n-3 = 2(5) -3 = 7 ------***

    Therefore, the original fraction was 5/7. ------answer.

    Check,
    2n/(d+8) =2/3
    2(5) / (7 +8) =? 2/3
    10/15 =? 2/3
    2/3 =? 2/3
    Yes, so, OK
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