Why is B = 4 + (1/3)(A-4) instead of 4 + (1/3)A?
Let's think about it this way: Lyle takes his money and leaves the room. There's now A dollars. Bob takes 4 dollars from that and puts it in his pocket. There's now A-4 dollars. Bob's a little selfish, so he decides to take one third of the remaining money. So he takes 1/3*(A-4), and since he already had 4 dollars in his pocket, he's got 4+1/3*(A-4) dollars now.