Incorrect Hotel Payments

At start, the 3 guests had $30. At the end, the 3 guests have $3, the bellboy has $2, and the hotel has $25. $30 = $1 + $1 + $1 + $2 + $25, and everybody is happy, as long as nobody opens their mouth.

There is no extra dollar.

The three men paid $30 for a room. The manager realized that the room only ought to have cost them $25, so he sent the bellhop back with $5 to be returned to them.

Out of the original $30, here's where it all went:

 Kept by motel:   $25
 Stolen by bellhop: 2
 Returned to men:   3
                  ---
 Total:           $30
                  ===

Another way of looking at it: The three men ended up paying a total of $9×3=$27. That's $25 for the room plus the $2 stolen by the bellhop.

The question tries to trick you into adding the $2 stolen by the bellhop to the total of $27 that the three men end up paying, for a total of $29, and then wondering why it doesn't add up to the original $30. But this is nonsense, as the $27 already includes the stolen $2 ($25 for the room plus the stolen $2 equals $27).

The $27 that the men ultimately end up paying, plus the $3 that was returned to them, adds up to the original $30. The $25 that the men were supposed to pay for the room, plus the $5 that the bellhop was supposed to return to them, equals the original $30.

Read more: 3 people pay $10 each for a motel room for $30. The manager over charges them and gives $5 in ones to the bellhop to return to them, he keeps $2 for himself. Where did the extra dollar go, if each person only paid $9? | Answerbag .

There is no missing dollar. The guests actually needed to pay $25 dollars altogether. They paid $30 instead, and received $3 back altogether.

So yes, they may have paid $27 altogether for the room, however, if the desk clerk took the $3 back from the guests, then she will have $28, and the bellboy will have $2, for a total of $30.

This question twists the truth of the story and uses it to state facts which are technically correct, however can be misleading. If you solved it, well done. If you didn't that's alright. I didn't understand this problem when I was solving it for the first time.

39 solutions before mine! I shall try to give the easiest way of thinking about this problem, though not the only way!

There are two parties, (A) Client (B) Hotel. Now from the problem, the Client party, consisting of three members, paid the Hotel party 27 USD. Now the Hotel party have a total of 27 USD = 25 (clerk) + 2 (bellboy)

So no missing dollar!

Broad analysis: So how did the question maker lead us to believe that there should be a missing dollar? Answer: Human psychology! We tend to leap into conclusions without looking into ALL the facts, specially the minor ones. By the narrative sentences we were led to the false concept that the bellboy is with the Client party, but it's absolutely not the case.

To explain it further, at 'level 0' level, let's think hotel payment as a gain and loss play ('level 0' reference: Kung Fu Panda). The client party had 30 USD, they gave it to the clerk, so their loss is 30 USD; in other words, their gain is -30 USD and the gain of clerk is +30 USD. Later the clerk gave 5 USD to the bellboy, so the gain of the clerk for this dealing is -5 USD and for the bellboy the gain is +5 USD. So the net gain of the clerk is (+30) + (-5) = +25 USD and the net gain of the bellboy is +5 USD. The rest follows; hence the proof of the answer.

Let us say that all three of them had 10💲when they came to the hotel.So when they paid for the room they didn't have any money with them.Now,when the bellboy gave all three of them 1💲each the total money they had was 3💲and the bellboy had 2💲and the desk lady had 25💲which adds up to3+2+25=30.

Well when the clerk give 5 dollars to bell boy, all the guests paid 25÷3=8.333333 When bell boy gives each of them 1$ that's 9.333333×3 =28 plus 2 $ in the pocket of bell boy
There is your 30

It is a lot easier to think about it when you think that they owed $25 and there were five extra dollars. They each payed 8 and a third dollars for a total of 25. They each got one dollar back from the bellboy so they each payed 9 and a third dollars for a total of 28 dollars with 2 dollars left over that the bellboy keeps which makes 30 without a missing dollar.

25÷3 does not equal 9. It's 9.something.

If the bill was 25 dollars and the bell boy took 3 dollars the total they paid would be 28$ and 2 to the tip. 25 +3 = 28 not 27. Dont rely on false infomation in the problam. So no missing dollar

Think of it this way: Each guest paid $10 and got $1 back. That's $9 each, for a total of $27. The room actually only cost $25, so some money is missing. How much? $27 - $25 = $2, which the bellboy kept. The question tricks you into subtracting the $27 from the original $30, to surmise that $3 is missing ($2 with bellboy and $1 missing), when in fact, you should subtract the actual cost of the room ($25) from the total they spent ($27), which results in the missing $2, which the bellboy has. There is no other missin $1.

Hotel money:25 bell boy:2 Money bell boy gave:3 TOTAL:30

Too easy man 30=25+2+3 u just have to understand the statement as 25 are already at hotel the bellboy had 5 he kept 2 and give out 3 which totals upto 30

The secret is in the fact that they give you what appears to be a solution with the 3×9 and the two dollars. You have to ignore that, and use common sense. It's actually just 30-5+3+2, which just gives you 30 again. This problem would be easy if it didn't include the reasoning behind there being a missing dollar.

number 29 is a bs number they threw in there. 9x3=27. the bellboy has 29 dollars which is here just to throw you off. so no money is missing they just added an irrelevant number to throw you off

The scenario is there to distract you. Strictly speaking, each guest had an 8.33 cost basis with the additional 1 dollar each returned by the bellboy. That's 9.33/person or 27.99 + the 2 dollars the bellboy took.

The problem is not adding up to $30, but rather "adding down" to $25. The bellboy's $2 brings the true room charge down from $27 to $25.

Write a solution. Ok so...at first they pay $10 each to make a total of $30 ($10 + $10 + $10 = $30), they it turned out that the total shoud have been $25 so the bellboy keeps $2 and gives a dollar to each guest and non dollar is missing ($25 + $2 + $1 + $1 + $1 = $30). Then it says it SEEMS that each guest paid $9, but the truth is that they paid (in total) $25 for the room, $2 for the bellboy (THAT MAKES $27) and then you have the $1 that was returned to each guest. So you can say that they actually spend $9 each (wich is a total of $27) but $2 of those went for the bellboy.