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Math Help - having problems solving an equation

  1. #1
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    having problems solving an equation

    Question: If P,Q and R are positive integers

    Then find Q P+ 1
    -------- = 25
    1 ----
    Q+ --- 19
    R

    Would appreciate it if someone could explain this.

    Thanks, sorry for taking your time
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  2. #2
    MHF Contributor kalagota's Avatar
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    excuse me, can you fix your equations?
    tnx
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  3. #3
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    damn it sorry,didn't come out the same way as it looked. Don't really know how to write equations like everyone else
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  4. #4
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    Hello,

    P+\frac{1}{Q+\frac{1}{R}}=\frac{25}{19}

    Since 25/19=1+6/19, you get P=1, \frac{1}{Q+\frac{1}{R}}=\frac{6}{19}.
    Inverting, you get Q+\frac{1}{R}=\frac{19}{6}.
    Extract the integer part, invert again and you get Q, R.

    Bye.

    (P.S. To write equations like everyone else, point the math formulae with your mouse cursor, and read the source before they get compiled.)
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  5. #5
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    Only got one thing to say speechless. Dude you are amazing thanks a lot!!!! helped me too ^^
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  6. #6
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Yaymath View Post
    damn it sorry,didn't come out the same way as it looked. Don't really know how to write equations like everyone else
    actually, you don't have to know that LaTex yet.. all you have to do is to use parentheses, brackets and braces to group properly the expressions..
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  7. #7
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    Well thnx a lot if anyones got another way of explaining why the answer became what it became. Would be perfect if i understood it at its fullest
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  8. #8
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    Hello,

    Since Q>=1 and R>0, you know that 0<1/(Q+(1/R))<1. Thus, P is the integer part and 1/(Q+(1/R)) is the rest.

    This is famous, in connection with the so called "Euclidean algorithm" to determine the greatest common divisor.

    Bye.
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