Dick has 5 loaves of bread. Nick has 3 loaves. The three share the bread equally with Albert. Albert gives Dick and Nick $8. What's a fair split? Dick and Nick share their food with Albert. Dick has 5 loaves of bread and Nick has 3 loaves. The three share the bread equally. Albert gives Dick and Nick 8 dollars, which they agree to share fairly.
How should Dick and Nick divide the eight dollars between them?
Dicks contributes $5/8$ of the loaves, while Nick contributes $3/8$. They each get $8/3$ of the bread.
Dick provided $5/8$ of Albert's meal so he should get \$5 and Nick \$3. Is that correct?
I'm not completely sure. It sort of feels right but not quite intuitively. I'm imagining the 8 loaves of bread combined into one. Split equally the bread still contains $5/8$ bread from Dick...
 A: Dick gets 7\$ and Nick gets 1\$. Here's why. Dick brought 5 loaves of bread, but ate $\frac83$ of them. Therefore, he gave $\frac73$ to Albert. On the other hand, Nick brought 3 loaves of bread, but ate $\frac83$ of them. Therefore, he gave $\frac13$ to Albert. So, Dick gave Albert $7$ times more loaves of bread, and therefore he deserves to get $7$ times more money.
A: Here is a quick answer.
There are 8 total loaves. Make them equal 24 pieces ( That means each bread has three slices). Albert eats 8 of them and gave them 8 bucks. That means each piece is worth 1$.
Since Dick had 15 slices of pieces of bread, he deserves 7 bucks, and the other guy deserves 1 buck. Note that Albert eats 7 slices from Dick's share and 1 slice from Nick's share.
Do you understand why?
A: So $\$8$ for $\frac 83$ loaves of bread seems fair. SO $\$ 1$ for $\frac 13$ of a loaf.
So Albert needs to pay Dick $5$ dollars and Nick $3$ dollars.  FIne, but what do Nick and Dick need to pay? Nick ate Dicks bread so Nick owes Dick something.  But instead of paying Dick directly Nick is just going to let Nick take some of Dick's share from Albert.
Each person ate $\frac 83$ loaves of bread so the should all come out $8$ dollars poorer either in bread the gave or money the paid for.
Albert contributed no bread at all so he pays entirely in dollars.  $\$8$ .
Dick contributed $3$ loaves or an $9$ dollars worth of bread. So he has already paid $\$9$ in bread.  But he ate $8$ dollars worth.  SO he is owed $\$1$ which he'll take in cash from Albert.
Nick contributed $5$ loaves or $\$15$ worth of bread. He ate $\$8$ worth.  So he is owed $\$7$ which he takes from Albert.
There are many ways of looking at this.
I:  Nick has $5$ loaves of bread.  He eats $\frac 83$ of them and gives the remaining $\frac 73$ to Albert. Dick has $3$ loaves of bread.  He eats $\frac 83$ of them and gives the remaining $\frac 13$ to Albert.  ALbert recieves $\frac 83$ loaves of bread and pays $8$ dollars for them.
II:  Albert ate $8$ portions of Bread.  He figures $5$ of them came from Dick so he gives Dick $5$ dollars, and $3$ of them came from Nick so he gives Nick $3$ dollars.  Nick ate $8$ portions of Bread and figure $5$ of them came from him so he pays himself $5$ dollars, and $3$ comes from Nick so he pays Nick $3$ dollars.  And Nick does the same; he pays Dick $5$ dollars and pays himself $3$ dollars.
So in the end: Dick has $5 + 5+ 5 - 3-5 = +7$ dollars.  And Nick has $3+3+3-5 -3 = +1$ and Albert has $-5-3=-8$.
III:  Everyone puts what they've got in a pot and takes back stuff of equal value.
Nick puts in $\$15$ worth of bread.  Dick puts in $\$9$ worth of bread.  Albert puts in $\$8$.
Nick takes back $\$8$ worth of bread and $\$7$ cash.  Dick takes out $\$8$ worth of bread and $\$1$.  Albert takes back $\$8$ worth of bread.
A: No, that's not right. Imagine that before Albert arrives, Dick and Nick each eat $\frac83$ loaves. Then Dick is left with $\frac73$ loaves and Nick is left with $\frac17$. So Dick should get $7$ of Albert's dollars.
A: 
Dick contributes $5/8$ of the loaves, while Nick contributes $3/8$.

This sounds intuitive but it is false. The question says they get $8/3$ loaves each.
A: Albert:  $8\$$ in exchange of  $\frac{8}{3}$ loaves of bread $\to$ ~3$/bread.
Dick: ($5-\frac{8}{3}) =\frac{7}{3}$  bread $\cdot 3 \$/bread= 7$\$
Nick: ($3-\frac{8}{3}) =\frac{1}{3}$bread $\cdot\$/bread 3 = 1$\$
