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23 February, 13:22

The ratio of two positive numbers is 3 to 4. if k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. what is the value of k

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  1. 23 February, 13:29
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    Let the two numbers be x and y

    x/y=3/4

    Therefore x=3z

    y=4z, where z is the GCF of x and y

    (3z+k) / (4z+k) = 4/5

    (3z+k) * 5 = (4z+k) * 4

    15z+5k=16z+4k

    k=z--->eq1

    3z+k+4z+k=117

    7z+2k=117--->eq2

    Using value of z from eq1 in eq2

    7k+2k=117

    k=117/9

    =13
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