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28 January, 17:28

A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/10 find the integers

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  1. 28 January, 17:45
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    x = 2y

    1/x + 1/y = 3/10

    Since we have a value for x, let's plug it into the second equation.

    1/2y + 1/y = 3/10

    Now, let's make the denominators equal.

    Multiply the second term by 2.

    1/2y + 2/2y = 3/10

    Multiply the final term by 0.2y

    1/2y + 2/2y = 0.6y/2y

    Compare numerators after adding.

    3 = 0.6y

    Divide both sides by 0.6

    y = 5

    Now that we have the value of the second integer, we can find the first.

    x = 2y

    x = 2 (5)

    x = 10

    Let's plug in these values in our equations to verify.

    10 = 2 (5) √ this is true

    1/10 + 1/5 = 3/10 √ this is true

    The first integer is equal to 10, and the second is equal to 5.
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