Number of bullets for each hunter [duplicate]

Question

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.

Answer 1

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.