One number is 6 times another. The sum of their reciprocals is 7/24. find the numbers

Question

One number is 6 times another. The sum of their reciprocals is 7/24. find the numbers

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Brielle 1 week 2021-10-05T03:43:22+00:00 2 Answers 0

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    0
    2021-10-05T03:44:26+00:00

    Answer:

    The numbers are 4 and 24

    Step-by-step explanation:

    Let the first number be x and the second number be y.

    since we were told that one number is 6 times another , let

    x = 6y ……………………………. equation 1

    The reciprocal of x = \frac{1}{x}

    The reciprocal of y = \frac{1}{y}

    The sum of the reciprocal will therefore be :

    \frac{1}{x}+\frac{1}{y}=\frac{7}{24} …………………………….. equation 2

    substitute x = 6y into equation 2 , equation 2 then becomes :

    \frac{1}{6y}+\frac{1}{y}=\frac{7}{24}

    The L.CM is 6y ,

    then we have \frac{1+6}{6y}=\frac{7}{24}

    \frac{7}{6y}=\frac{7}{24}

    since they have the same numerator , we will equate the denominator , that is

    6y = 24

    divide through by 6

    y = 4

    substitute y = 4 into equation 1 to find the value of x , that is

    x = 6(4)

    x = 24

    Therefore : The numbers are 4 and 24

    Check:

    x = 6y

    24 = 6(4) = 24

    \frac{1}{x}+\frac{1}{y}=\frac{7}{24}

    \frac{1}{24}+\frac{1}{4}

    L.C.M = 24

    so we have

    \frac{1+6}{24}

    = \frac{7}{24}

    0
    2021-10-05T03:45:15+00:00

    Answer:

    x=24, y=4

    Step-by-step explanation:

    x=6y

    1/x+1/y=7/24,

    1/6y+1/y=7/24

    1/6y+6/6y=7/24

    (1+6)/6y=7/24

    7/6y=7/24, then

    6y=24

    y=24/6

    y=4

    x=6y=6*4=24

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