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

mathdaughter

New member
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

Elite Member
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.

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

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

$$\displaystyle 0.936x = y.$$

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

Elite Member
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

New member
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

Junior Member
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

Elite Member
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

New member
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

Elite Member
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.

Jomo

Elite Member
I was wrong.

0.936x = y

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

so x = 125 is the fewest?