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Math Help - Percent help

  1. #1
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    Percent help

    There is 2 positive numbers
    1 number is p% of the other

    How many percent is those numbers geometric mean from arithmetic mean?


    Answer is (20√(10) / p+100) %

    How to get there? Been struggling with this so long. Its high school year 12 math.
    Sorry for my bad english. (also for bad title, i dont know English definition for that)
    Last edited by Trolo; March 25th 2014 at 07:12 AM.
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  2. #2
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    Re: Percent help

    Quote Originally Posted by Trolo View Post
    There is 2 positive numbers
    1 number is p% of the other

    How many percent is those numbers geometric mean from arithmetic mean?


    Answer is (20√(10) / p+100) %

    How to get there? Been struggling with this so long. Its high school year 12 math.
    Sorry for my bad english. (also for bad title, i dont know English definition for that)
    you have two numbers $x$ and $y=\dfrac{px}{100}$

    The arithmetic mean is $\dfrac{x+y}{2}=\dfrac{100x+px}{2\cdot 100}=\dfrac{(100+p)x}{200}$

    The geometric mean is

    $\sqrt{xy}=\sqrt{\dfrac{px^2}{100}}=\dfrac{x\sqrt{ p}}{10}$

    I don't really know how to interpret your actual question, but given these two means you can figure out the ratio you are after.
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  3. #3
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    Re: Percent help

    Yea got the ratio! Thanks
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