Four elderly men retired to live in log cabin in rural area?

Question

As winter approached the men decided that they must burn fire in the fireplace to stay warm.

First man went into the forest and brought back 3 sacks od firewood.
Second man brought back 4 sacks od firewood.
third man brought back 5 sacks od firewood.

The fourth man said:
'We've got enough firewood already, do not we? Instead of bringng more firewood let me pay the three of you total $24 for your efforts',
and everyone agreed.

How should the three men divide $24?

Answer 1

There are 12 sacks of wood, so the nominal share should be 3 sacks each for the 4 men.

The fourth man agreed to pay $24 instead of bringing 3 sacks of wood. That makes a sack equivalent to $8.

The first man brought 3 sacks which is exactly the required share per person, so he should get nothing extra.
The second man brought 1 extra sack (essentially on behalf of the 4th man) so should get paid $8 for the exta sack.
The third man brought 2 extra sacks (again on behalf of the 4th man) so should get paid $16.

That is the fair way to distribute the money.
1st man --> 3 sacks (value = $24 equivalent to his required share, no refund necessary)
2nd man --> 4 sacks (value = $32, deserves a refund of $8)
3rd man --> 5 sacks (value = $40, deserves a refund of $16)
4th man --> paid $24 equivalent to the value of 3 sacks.

Answer 2

All four men share equally in the value of the wood and each consumes that value of wood. Change the question to read sandwiches to think of how much each consumes. There are 12 sandwiches with each man eating 3. The fourth man has now spent $24 for his three sandwiches, so the value of 1 sandwich (sack of wood) must be $8. The first man consumes exactly what he brought, so he gets none of the money. The second man contributes 1 sandwich (sack of wood) to the fourth man, so he is entitled to $8. The third man contributes 2 sandwiches (sacks of wood) to the fourth man, so he is entitled to $16.

So the division of the money goes like this:
The first man contributes 3 sacks of wood worth $24 and consumes 3 sacks of wood worth $24. He is entitled to no additional money.
The second man contributes 4 sacks of wood worth $32 and consumes 3 sacks of wood worth $24 So he should get $8 to balance his contribution.
The third man contributes 5 sacks of wood worth $40 and consumes 3 sacks of wood worth $24. So he should get $16 to balance his contribution.
The fourth man contributes $24 and consumes 3 sacks of wood worth $24.

Answer 3

The fairest way is to determine the value for a single sack of wood and pay the men according to the number of sacks they brought in:

3+4+5 = 12 sacks of wood total, so each sack is worth 24/12= $2 per sack.

So the first man gets 3($2)= $6
the second man gets 4($2)= $8
and the third man gets 5($2)=$10

Answer 4

They should split it 3 ways since each man brought back some wood.
Man 1 brought back 3/12 of all wood.
3/12= 0.25
Man 2 brought back 4/12 of all wood.
4/12 = 1/3
Man 3 brought back 5/12 of all wood.
Man 1 should get 3/12 of $24, which is $6.
Man 2 should get 4/12 of $24, which is $8.
Man 3 should get 5/12 of $24, which is $10.

Answer 5

They brought it in a 3:4:5 ratio, so they should split it like that: $6, $8, and $10.

Answer 6

First man gets $ 6,
Second man gets $ 8 and
Third man gets $ 10.