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Math Help - Percents Word Problem Translation

  1. #1
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    Percents Word Problem Translation

    Hi All,
    Question: "x is what percent of y percent of z, in terms of x,y,z"

    Y percent of z = \frac{y}{100}.z

    X percent of y percent of z = \frac{w}{100}.\frac{y}{100}.z

    This is where it gets confusing for me.

    This translates to x = \frac{w(\frac{yz}{100})}{100}

    Question one: I'm not sure how \frac{w}{100}.\frac{y}{100}.z transforms into \frac{w(\frac{yz}{100})}{100}

    Question two: I'm not sure how \frac{w(\frac{yz}{100})}{100} transforms into  w = \frac{100x}{\frac{yz}{100}}

    Question three: I'm not sure how  w = \frac{100x}{\frac{yz}{100}}transforms into  w = \frac{10,000x}{yz}

    There just seems to be jumps in logic that I'm not getting.

    Thx,
    D
    Last edited by CaptainBlack; April 1st 2011 at 07:53 AM.
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  2. #2
    Super Member Quacky's Avatar
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    Question one: I'm not sure how \frac{w}{100}.\frac{y}{100}.z transforms into \frac{w(\frac{yz}{100})}{100}
    It is a very strange setup!

    \frac{w}{100}\times\frac{y}{100}\times~z

    =\frac{w}{100}\times\frac{yz}{100}

    =\dfrac{\frac{w\times~yz}{100}}{100}

    =\frac{w\times\frac{yz}{100}}{100}

    Although why you'd set something out so poorly is beyond me!

    Question two: I'm not sure how \frac{w(\frac{yz}{100})}{100} transforms into  w = \frac{100x}{\frac{yz}{100}}
    Again, this is a dreadful approach! I'd not even bother going whatever route they've taken. Starting at:

    x=\frac{w(\frac{yz}{100})}{100}, multiply both sides by 100:

    100x=w\times\frac{yz}{100} Then do it again:

    10000x=w\times~yz Now divide both sides by yz
    <br />
\frac{10000x}{yz}=w ...which is their final answer.

    Do you follow my method? The approach you've been shown is really quite bad.
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by dumluck View Post
    Hi All,
    Question: "x is what percent of y percent of z, in terms of x,y,z"

    Y percent of z = \frac{y}{100}.z

    X percent of y percent of z = \frac{w}{100}.\frac{y}{100}.z

    This is where it gets confusing for me.

    This translates to x = \frac{w(\frac{yz}{100})}{100}

    Question one: I'm not sure how \frac{w}{100}.\frac{y}{100}.z transforms into \frac{w(\frac{yz}{100})}{100}
    \frac{w}{100} \cdot \frac{y}{100}\cdot z = \dfrac1{100} \cdot w \cdot \left( \dfrac{y z}{100} \right) = \dfrac1{100} \cdot \left( w \cdot \left( \dfrac{y z}{100} \right) \right) = \dfrac{\left( w \cdot \left( \dfrac{y z}{100} \right) \right)}{100}

    Question two: I'm not sure how \frac{w(\frac{yz}{100})}{100} transforms into  w = \frac{100x}{\frac{yz}{100}}
    x=\dfrac{w(\frac{yz}{100})}{100}~\implies~100x=w(\  frac{yz}{100})~\implies~w=\dfrac{100x}{\frac{yz}{1  00}}
    Question three: I'm not sure how  w = \frac{100x}{\frac{yz}{100}}transforms into  w = \frac{10,000x}{yz}

    There just seems to be jumps in logic that I'm not getting.

    Thx,
    D
    I'll leave the last step for you: You have to divide a term (100x) by a fraction. How do you do this usually?
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  4. #4
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    Quote Originally Posted by earboth View Post
    \frac{w}{100} \cdot \frac{y}{100}\cdot z = \dfrac1{100} \cdot w \cdot \left( \dfrac{y z}{100} \right) = \dfrac1{100} \cdot \left( w \cdot \left( \dfrac{y z}{100} \right) \right) = \dfrac{\left( w \cdot \left( \dfrac{y z}{100} \right) \right)}{100}



    x=\dfrac{w(\frac{yz}{100})}{100}~\implies~100x=w(\  frac{yz}{100})~\implies~w=\dfrac{100x}{\frac{yz}{1  00}}


    I'll leave the last step for you: You have to divide a term (100x) by a fraction. How do you do this usually?
    multiply the reciprical of the denoiminator. Thanks to you both.
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