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The problem is as follows:

Two hunters make a stop in the forest to eat their breads. One of them has 5 breads and the other has 3 breads. Suddenly, another hunter appears, who has no bread at all. In a gesture of friendship they decide to share all their breads equally. When they finish, the guest hunter gives them 8 bullets to be distributed proportionally. How many bullets corresponds to each one?

The choices in my book are:

  1. 5 and 3 bullets
  2. 6 and 2 bullets
  3. 4 and 4 bullets
  4. 7 and 1 bullets

I found this problem in my Reason and Logic book from 2000's and from the topic presented it seems to be an adapted version from a reprinted edition of Martin Gardner's 70's book on Puzzle Carnival.

What I attempted to do in order to solve this problem was to use proportions:

Let's say:

hunter 1: $5k$

hunter 2: $3k$

This lets k be used to determine how to proportionately share ammunition.

Adding these and equating to the bullets yields:

$5k+3k=8$

Hence:

$k=1$

and the number of bullets shared between them will be 5 and 3. But my book states the right answer is the fourth option. I wonder why this is. Did I interpret the problem wrong, or forget to read between the lines?

Can someone help me with this? Please give answers that are as detailed as possible and include a step by step solution to help me understand.

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  • $\begingroup$ bread is a collective noun. you want to say "3 loaves of bread" and not "3 breads". $\endgroup$ – matt Nov 5 '20 at 18:14
  • $\begingroup$ @matt Sorry about that. I'm improving my grammar skills, it is not easy. $\endgroup$ – Chris Steinbeck Bell Nov 8 '20 at 2:13
  • $\begingroup$ thats perfectly okay (oh look at that I missed the apostrophe lol) $\endgroup$ – matt Nov 8 '20 at 7:37
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The key here is to draw pictures. Let's say we have the two initial hunters, with their bread pieces represented as numbers:

o   o
(5) (3)

Then the third hunter appears:

o   o   o
(5) (3) (0)

In order to "share all their breads equally", they will need to distribute the bread so that each person has an equal amount of bread. Therefore, since the total amount of bread is 8 (5 + 3), they each will have 8/3 = 2 and 2/3 pieces of bread.

To get this amount of bread:

  • The first hunter starts with 5 and ends with 2 and 2/3. (- 2 and 1/3)
  • The second hunter starts with 3 and ends with 2 and 2/3. (- 1/3)
  • The third hunter starts with 0 and ends with 2 and 2/3. (+ 2 and 2/3)

So the first hunter gives up 2 and 1/3 pieces, and the second hunter only gives up 1/3 pieces to make this happen. If each x is 1/3 a piece of bread, we can illustrate that like this:

Hunter 1        Hunter 2
xxx xxx x       x
(7)             (1)

As a result, when the third hunter distributes bullets "proportionally," he gives them a number of bullets that makes sense with the proportional amounts of bread they gave up: 7 and 1.

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  • $\begingroup$ Sorry for the delay in leaving a comment. But it was very nice of you to include a sketch for me to understand. However I think there's missing a key element which is why do you subtract those $\frac{8}{3}$ from the two hunters?. I think the reason is that bread is an edible thing, hence the problem assumes that you only give with what you're left off after eating it (although this part doesn't seem reasonable as you share what you had not what you're being left off). $\endgroup$ – Chris Steinbeck Bell Nov 8 '20 at 2:11
  • $\begingroup$ By the time when we get that one has $\frac{7}{3}$ and the other $\frac{1}{3}$ equals a proportion of $7$ to $1$. Which is done by dividing both or making those as integers, isn't it?. I've done this by multiplying it by $3$ and the proportion is held. Maybe you want to include my earlier comments as part of your answer. $\endgroup$ – Chris Steinbeck Bell Nov 8 '20 at 2:13

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