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find two numbers whose sum is 25 and the sum of whose reciprocals is one sixth

  • math -

    Solve this pair of equations:
    x + y = 25
    1/x + 1/y = 1/6

    Rewrite as
    1/x + 1/(25-x) = 1/6
    [(25-x) + x]/[x(25-x)] = 1/6
    150 = x(25-x)
    x^2 -25x + 150 = 0
    (x-30)(x-5) = 0
    One more step

  • math -

    I tried to finish drwls solution and verify the answers, but they would not check out.

    After my second cup of coffee, I realized that my good collegue made what we used to call "wishful thinking solutions" error.

    the factors would be (x-15)(x-10)
    and we get symmetric solutions, that is, when x=15, y=10 and when x=10 y = 15

  • math -

    Correct, my mistake.

  • math -

    x+25x+150=0

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