Another Way of Looking At It...
I could ask why you are adding amounts spent and amounts received. The men
spent $27, the bellboy
received $2. Let's look at the total amounts spent and received. The men initially
spent $10 each, for a total of $30. The hotel received the $30, but only kept $25, returning the other $5, so the hotel
received $25. The bellboy
received $2 (apparently a carrying charge!), and the men each
received a $1 refund (for a total of $3). Seen this way, the men spent $30, and the hotel received $25, the bellboy received $2, and the men received $3, for a total received of $30.
If we wanted to get more complicated, the men spent $30 on the room, which the hotel received. The hotel then spent $5 on the refund, of which the bellboy received $2 and the men received $3. Then the total spent is $35 ($30 by the men and $5 by the hotel), and the total received is $35 ($30 by the hotel, $2 by the bellboy, and $3 by the men as a refund).
Or We Could Look at an Extreme Case...
What happens if we assume the bellboy was completely dishonest, and decided to keep the $5? Then the question would have been:
"But when he does that and gives each man nothing, that means they still paid $10.00 each for the room, which is a total of $30.00; plus the $5.00 the Bell Boy pocketed is a total of $35.00. But they only gave the desk clerk $30.00! Where did the extra $5.00 come from??"
This is either a mathematical proof that crime really does pay, or, more likely, a very suspect statement. That's why the numbers in the original were chosen to make it look like it almost worked. That way you go along with the misdirection, get misled by the wrong calculation, and are confused by the result.
Of course, what actually happened (in our modified case) was that each man paid $10 for the room, for a total of $30.00, of which the hotel got $25 and the bellboy got $5.
In Summary...
This problem is an example of using quick-talking to convince people to accept what you're saying, rather than checking the calculations themselves.
Reading that last statement prompts me to read again the playing directions for the PowerBall Lottery. Maybe there's a glitch there.
OpenMinded - Some things still boggle me.