# Distributing an item equally.

For the following question

A $10$ foot plank of wood is cut to give three equal lengths with a shorter length left over. Which is more

a)The length of one of equal pieces

b) $3$ feet

Now here is how I am solving it --> Each piece gets =$\frac{10}{3}$ and remaining is $1$ foot. So I think both are equal. However the text states that "Not enough information is given to solve the problem" Why is that.

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How do you know each equal piece should be 10/3 of a foot? Besides, that'd give no remaining length. What if I cut 3 3-foot lengths, leaving 1 foot left over? What other lengths could I pick to still satisfy the requirement? – Kevin Carlson Aug 3 '12 at 21:08
How would you divide $10$ feet equally into $3$ pieces ? $\frac{10}{3}$ ? right ? – MistyD Aug 3 '12 at 21:11
@KevinCarlson 10 feet distributed over 3 pieces equally leaves 1 foot behind – MistyD Aug 3 '12 at 21:13
For example, the lengths could be $3.1,3.1,3.1,0.7$; or they could be $2.6,2.6,2.6,2.2$. – David Mitra Aug 3 '12 at 21:13
Hmm.. Yeah I agree.. Thanks – MistyD Aug 3 '12 at 21:15

You have $10=3x+y$, where $x$ is the number of feet of each of the lengths cut off and $y$ is the length left over. And you have $y<x$, and so $10 = 3x+y < 4x$. This is all the information you have. So why does this mean that you can't infer the answer?

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Draw the piece of wood, with cuts roughly as specified. Maybe each of the three equal pieces is $3.1$ feet. That would give $0.7$ feet left over. Note that $3.1 \gt 3$.

Maybe each of the three equal pieces is $2.9$ feet. That would give $1.3$ feet left over. Note that $2.9 \lt 3$.

Maybe each of the three equal pieces is $3$ feet. that would give $1$ foot left over.

So from the information we have been given, it is possible that the equal pieces are each less than $3$ feet, or are bigger than $3$ feet, or exactly equal to $3$ feet. So there is not enough information to answer the question.

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