Can anyone explain 'The Missing Dollar' Conundrum, please?

[Kiki-frog]

This was on the Simon Mayo R2 show this evening. I understood the maths of the problem, but not the answer that was given.

The story is that three men check into a hotel for the night. The room rate is $30, so they pay $10 each. Once they've gone up to the room, the receptionist realises that he's overcharged them as the room rate should only be $25. Because they've paid separately, he realise he can't refund them equally, so he gives them back one dollar each and pockets the other two himself.

So now they've each paid $9 dollars for the room, a total of $27, and the receptionist has kept $2, making $29 in all. So where's the missing dollar?

The guy on the radio explained why this thinking was mathematically wrong, but I couldn't get my head round it. Can anyone explain in idiot language, please?

[TheNovice]

they haven't paid $9, they've all paid $9 & 2/3 (two third dollars)

[HowardKennitby]

There is no missing dollar

The hotel has $25 The guests have $1 each and the receptionist has $2. Total = $30

[mike11111]

The fallacy is that they have not paid $9 for the room but $8.33. They have paid $9 for the room plus what the receptionist has pocketed.

[factor-fiction]

It's a nonsensical calculation because there is absolutely no logic in adding the 27 to the 2. The hotel has $25, the receptionist has $2 and the men have $3- so all $30 is accounted for.

[bert_h]

The three guys have each paid $9, which is $27 all right, but the $2 that the receptionist kept is PART OF that $27. So if you add it instead of subtracting it, you get $29 which completely illogically consists of $25 plus another $2 counted twice. Since that's an illogical sum, then whatever you try to compare it with, it is sure to turn out nonsense of one kind or another.

[mike11111]

I remember this one from my childhood, only it was three men in a restaurant paying for their meal. This was before decimal currency when a pound was exactly divisible by three.

[Kiki-frog]

Of course I knew that really.....

Seriously, thanks everyone. That was driving me nuts. I'm not at all good with numbers, but I think I've got it now.

[Psybbo]

$30-3=27-2=25
no missing $