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

mathdaughter

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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,
 

JeffM

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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.
-----

thanks,
Yes you do.

First set up an equation.

\(\displaystyle x = \text { number of persons surveyed.}\)

\(\displaystyle y = \text { number of persons who completed survey.}\)

\(\displaystyle 0.936x = y.\)

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?
 

Jomo

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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.
 

mathdaughter

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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?
 

j-astron

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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.
 

JeffM

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3,232
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

\(\displaystyle 0.936 * 105 = 98.28.\) NOT A WHOLE NUMBER.

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

Let's think like this:

\(\displaystyle 0.936x = y \implies 0.936 = \dfrac{y}{x} \implies 5 * 0.936 = 4.68 = 5 * \dfrac{y}{x} \implies\)

\(\displaystyle 5 * 4.68 = 23.4 = 5 * 5 * \dfrac{y}{x} = 25 * \dfrac{y}{x} \implies\)

\(\displaystyle 5 * 23.4 = 117 = 5 * 25 * \dfrac{y}{x} = 125 * \dfrac{y}{x} \implies WHAT?\)

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.
 
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mathdaughter

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I was wrong.

0.936x = y

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

so x = 125 is the fewest?
 

JeffM

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Jomo

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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.
 
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