Three people are staying at a cheap hotel which charges them $30 for a room. They split the cost $10 dollars each. The next day, the manager notices they were overcharged; the actual cost should have been $25. The manager gives $5 to the bellhop to give back to the three guests. What happens next: on his way to the room, the bellhop decides to pocket $2 and gives back $5-$2 = $3 to the guests ($1 each). So, in reality, each guest did not pay $10. Each got a $1 back. So each paid $10 -$1 = $9 to stay in the room. Their total expense is therefore 3 x $9 = $27. The bellhop has pocketed $2.

PROBLEM: Counting back all the dollars, we have: $27 (guests) + $2 (bellhop) = $29, not $30 anymore So, where is the missing dollar?

(a) Express below your explanation and conclusion after completing the tables. Explain what is really going on here with the money exchange.

(b) Explain in sufficient detail the kind of quantative business model underlying the overall thinking here?

	Step 1: At the start:
		Guests	Manager	Bellhop	Balance
	Step 1 results	-30	30	0	0
	Totals	-30	30	0	0
	Step 2: The manager gives $5 to the bellhop:
		Guests	Manager	Bellhop	Balance
	Step 1 totals	-30	30	0	0
	Step 2		-5	5	0
	New totals	-30	25	5	0
	Step 3: the bellhop gives $3 back to the guests:
		Guests	Manager	Bellhop	Balance
	Step 1 totals
	Step 2 totals
	Step 3
	Final totals