wheres the missing money?

[knotty man]

3 salesmen go to a hotel for the night. but, there is only 1 room vacant. the mgr. tells them he can let them have it for 30 bucks. they each give 10 bucks a piece to get the room a they start to bed down for the night. but, the mgr realizes he overcharged them. the room was only 25 dollars. he gives the bellboy 5 dollars and tells him to give it back to the gentlemen. the bellboy realizes 5 dollars wont divide into 3 guys ,so he pockets 2 dollars and gives the gents back each a dollar. therefore each man paid 9 dollars each. ok 9 dollars tiomes 3 guys = 27, plus the 2 dollars the bellboy pocketed=29 dollars. wheres the other dollar?

[Holeshot]

with the manager. Because 3 doesn't factor in to $25. Each salesman actually paid $9.33 for the room.

[Chainsaw Anthropologist]

I think you should look at the equation in this manner:

3 salesmen x 10 = 30 (original payment)

revised refund statement....

1 owner +25, 1 bellboy +2, 3 salesmen (1 each) total +3 =30 (refund/payment)

There is no missing money.

It is possible to manipulate the second equation and derive a 27.

o=25, bb=2, s=3
o+bb+s = 30 therefore
o+bb = 30-s (27)

[slocum]

That's right. The $2 is not added to the $27, it is subtracted. From a purely symbolic perspective, it's the distribution law.

30 - 5 = 25
30 - (3 + 2) = 25
30 - 3 - 2 = 25
27 - 2 = 25

[runswithscissors]

I suddenly have a headache.....must find the Grey Goose bottle.....

[xxnubyxx]

Let me try it in layman term. Each salesman paid 10 dollars, so 10 +10 +10 = 30
They get back 3 dollars, so -1, -1, -1, totaling 27, in other word: 9+9+9=27.
The deception here is, if the total they paid out is 27, and the bell boy kept 2, where is is the missing 1. Graphically you can see the deception. From the total pool of 30, the salesmen kept the 3 in red. The bellboy kept the 2 in green. And the manager kept the 25 in blacks. The answer is the "missing 1" is a mathematical illusion coming from the idea that 9*3=27+2=29 should equal 10*3=30. It's a good trick question, but getting 3 dollars back from your original 30 changes the total sum to 27 (30 no longer applies as the total sum), which is the same as paying 9 each. Out of that 27 total, the bellboy kept 2 and the Manager kept 25. Adding the 27 to the 2 is an illusion of trying to get 30, because the bellboy made the mistake of not returning the total 5, but keeping 2.

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