Question

A little fun question
Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself. Each guest got $1 back: so now each guest only paid $9; bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29.

Answer 1

if the guests originally handed over $30, what happened to the remaining $1?

Answer 2

Okay, I think I got it. The money with the bellhop is unimportant, in the end they all pay $9, which is 27 but they were each given a dollar back, so they would have $27 + $3 which would give them 30.

Answer 3

What's the problem with the given train of thought. Is it violating any principle of math?

Answer 4

the problem is obscuring mathematical logic with words,

we want to determine the total money, at the end of all transactions:
at the end, the guests spend 27, so they are left with 3
of the 27, 2 is with the bellboy and 25 with the cashier.

guest+bellboy+cashier = 3+2+25=30

29 is obtained by 27+2
i.e expenditure of guests+gain of bellboy
this is a meaningless quantity

Answer 5

if you are not convinced that 29 is meaningless,

(expenditure of guests 27) = (bellboy 2) + (clerk 25)

add (bell boy 2) to both sides


(expenditure of guests 27) + (bell boy 2) =2 (bellboy 2) + (clerk 25)

thus
29 = 2 (bellboy 2) + (clerk 25)

29$ is the twice the money of the bell boy + clerk, which is a meaningless quantity