Puzzle – Ali and 8 Loaves

Question:
Two men were dining together. Five loaves of bread were brought by the first man, and three by the second. Ali, a third man, arrived and joined them. They ate all eight loaves together. Ali offered the men 8 coins as a thank-you gift before he left. The first man offered to take 5 coins and give his partner 3, but the second man objected and demanded an equal share of the half of the total, or 4 coins. The first one declined. They approached Ali and enquired about the just resolution. I believe it is best for you to accept your partner’s offer, Ali said to the second man. The man demanded justice but was refused. “Then I declare that who offered 5 loaves takes 7 coins, and who offered 3 loaves takes 1 coin,” Ali responded. Can you tell me why this was fair in the first place?

Solution:
The two men contributed three and five loaves of bread, respectively. Each loaf was divided into 3 equal parts (1/3rds), so there are eight times 3 = 24 thirds. If we assume that each man ate the same amount of bread, 1/3rd of the total 24 thirds, each man ate 8 of the thirds. This means that all three men would have shared the loaves equally eating 2 ⅔ loaves each. 
Person 1 contribution = 5 – 2 ⅔ = 2 ⅓
Person 2 contribution = 3 – 2 ⅔ = ⅓ 
On calculating their net contributions, person 1 gave 2 ⅓ loaves and person 2 who gave just ⅓.
This means that Ali ate only one of thirds of the second man’s bread and seven of the thirds of the first man’s bread. 
So, a just division is one coin for the man contributing 3 loaves and seven coins for the man contributing 5 loaves.