Problem Solving

ejager wrote: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives a $4 plus one half of what remains. Next, Bob receives $4 plus one third of what remains. Finally, Chloe receives the remaining $32. How much money did Bob receive?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 52

Expert reply-
My solution is below. Note that we don't need to consider Ann's portion in the solution. We can just let K be the money remaining after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we get K - Bob's $ = 32
The equation is K-4 - (K-4)/3 = 32
Solve for K (K=52) and then determine Bob's portion ($20).
The answer is, indeed, A

I don't understand why in the equation K - B= 32, if B= 4+(k-4)/3
when you plug in B for K-B shouldn't the negative carry through to all terms?

So why isn't it:
K - (4+(k-4)/3 =32
K - 4 - K+4/3 = 32
K - K+4/3 = 36
K-K =O which doesn't make sense?