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17 September, 13:54

He sum of the numerator and the denominator of the certain fraction is equal to 4,140. when the fraction was reduced, the result was 7 13. what was the original fraction?

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  1. 17 September, 14:56
    0
    1449/2691

    Step-by-step explanation:

    Let the fraction be x/y. Then, we have two conditions:

    (1) x + y = 4140

    (2) x/y = 7/13

    (3) 13x = 7y Multiplied each side by the lcd (13y)

    (4) y = 4140 - x Subtracted x from each side of (1)

    13x = 7 (4140 - x) Substituted (4) into (3)

    13x = 28 980 - 7x Distributed the 7

    20x = 28 980 Added 7x to each side

    (5) x = 1449

    1449 + y = 4140 Substituted (5) into (1)

    y = 2691 Subtracted 1449 from each side

    The original fraction was 1449/2691.

    Check:

    (1) 1449 + 2691 = 4140 (2) 1449/2691 = 7/13

    4140 = 4140 7/13 = 7/13

    OK.
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