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Thread: Enough conditions for this question? smallest number if exactly 93.6% answered

  1. #1

    Enough conditions for this question? smallest number if exactly 93.6% answered

    For the following question, do we have enough conditions to get the solution?

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    What is the fewest number of people surveyed if exactly 93.6% of the people surveyed actually completed the whole survey? Explain your answer or show your work.
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    thanks,

  2. #2
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    Quote Originally Posted by mathdaughter View Post
    For the following question, do we have enough conditions to get the solution?

    -----
    What is the fewest number of people surveyed if exactly 93.6% of the people surveyed actually completed the whole survey? Explain your answer or show your work.
    -----

    thanks,
    Yes you do.

    First set up an equation.

    [tex]x = \text { number of persons surveyed.}[/tex]

    [tex]y = \text { number of persons who completed survey.}[/tex]

    [tex]0.936x = y.[/tex]

    Can you give a survey to a fraction of a person?

    Can you have a fraction of a person complete a survey?

    So x and y must be positive whole numbers. Now what?

  3. #3
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    Quote Originally Posted by mathdaughter View Post
    For the following question, do we have enough conditions to get the solution?

    -----
    What is the fewest number of people surveyed if exactly 93.6% of the people surveyed actually completed the whole survey? Explain your answer or show your work.
    -----

    thanks,
    78% means 78/100. 78.5%=78.5/100 or 785/1000

    Do the same for 93.6% and then reduce and you'll have your answer. Post back with your work so it can be verified as correct or to show where you went wrong.
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

  4. #4
    0.936x = y;

    The fewest x should be 105 to make y a whole number. Because 6*5 is ended with 0, so 93.6*5 will a whole number, then 105 must be the smallest. Am I correct?

  5. #5
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    Quote Originally Posted by mathdaughter View Post
    0.936x = y;

    The fewest x should be 105 to make y a whole number. Because 6*5 is ended with 0, so 93.6*5 will a whole number, then 105 must be the smallest. Am I correct?
    If 105 people were surveyed, then 0.936*105 =98.28 people completed the survey?

    That's a fractional number of people. So no, that is not the right answer.

    0.936x = y

    divide both sides of the equation by x:

    0.936 = y/x

    You want the smallest whole numbers y and x that make this equation true. As Jomo hinted, y = 936 and x = 1000 certainly make the equation true, but they're not the smallest numbers that do. So you need to reduce the fraction 936/1000 to an equivalent one with the smallest possible values.

  6. #6
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    Quote Originally Posted by mathdaughter View Post
    0.936x = y;

    The fewest x should be 105 to make y a whole number. Because 6*5 is ended with 0, so 93.6*5 will a whole number, then 105 must be the smallest. Am I correct?
    You are thinking in the correct direction, BUT

    [tex]0.936 * 105 = 98.28.[/tex] NOT A WHOLE NUMBER.

    The 5 helps with the 0.006, but not with 0.93.

    Let's think like this:

    [tex]0.936x = y \implies 0.936 = \dfrac{y}{x} \implies 5 * 0.936 = 4.68 = 5 * \dfrac{y}{x} \implies[/tex]

    [tex]5 * 4.68 = 23.4 = 5 * 5 * \dfrac{y}{x} = 25 * \dfrac{y}{x} \implies[/tex]

    [tex]5 * 23.4 = 117 = 5 * 25 * \dfrac{y}{x} = 125 * \dfrac{y}{x} \implies WHAT?[/tex]

    EDIT: Jomo's way is perhaps easier arithmetically, but perhaps less intuitive relative to your personal thought process. There are frequently several ways to solve a problem.
    Last edited by JeffM; 03-04-2018 at 11:10 PM.

  7. #7
    I was wrong.

    0.936x = y

    y/x = 0.936 = 936/1000 = 468/500 = 234/250 = 117/125

    so x = 125 is the fewest?

  8. #8
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    Quote Originally Posted by mathdaughter View Post
    I was wrong.

    0.936x = y

    y/x = 0.936 = 936/1000 = 468/500 = 234/250 = 117/125

    so x = 125 is the fewest?
    Yes. Well done.

  9. #9
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    Quote Originally Posted by mathdaughter View Post
    I was wrong.

    0.936x = y

    y/x = 0.936 = 936/1000 = 468/500 = 234/250 = 117/125

    so x = 125 is the fewest?
    Yes!! Just reduce 936/1000 to get your answer.
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

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