Missing dollar!

Tom Anderson

Artistry in Titanium
See if you can figure this one out...

Three salesmen go to a hotel. The room rate is $30, and they each pay $10. Later that night the desk clerk realizes that the room is only $25 so he gives $5 to the bellboy to split among the 3 guys. The bellboy did not know how to split the $5 among the 3 men so he kept $2 for himself and gave $1 each to each man.
So… with the refund, each salesman paid $9 for a total of $27, the bellboy kept $2. This adds up to $29. Where is the missing dollar?
 
10+10+10=30 (Initial Payment)
30-5=25 (refund of $5)
25+2=27 (bellboy keeping $2)
27/3=9 (amount paid by each person)

The dollar was lost in the order of operations.
[(10+10+10-5)+2]/3 (10 from each man, $5 refund, $2 kept by bellboy, divided by 3)
is not the same as saying
(9*3)+2 ($9 each man paid, times 3, plus the $2 the bellboy kept)


At least that's how I see it... Dunno if I'm right or not. :p
 
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See if you can figure this one out...

Three salesmen go to a hotel. The room rate is $30, and they each pay $10. Later that night the desk clerk realizes that the room is only $25 so he gives $5 to the bellboy to split among the 3 guys. The bellboy did not know how to split the $5 among the 3 men so he kept $2 for himself and gave $1 each to each man.
So… with the refund, each salesman paid $9 for a total of $27, the bellboy kept $2. This adds up to $29. Where is the missing dollar?

The $2 the bellboy kept is part of the $27 the three men paid. You can't add it to the $27.

The men paid $27 for a $25 room (with $2 to the bellboy). 27 + 3 (refund) = 30. Or 30 - 3 (refund) = 27, 27 - 2(bellboy) = 25 (price of the room).

Or in other words So... with the refund, each salesman paid $9 for a total of $27, $2 of which went to the bellboy.



Just joined by the way, took me a few minutes, couldn't walk past this one till I figured it out.

T
 
Or in other words So... with the refund, each salesman paid $9 for a total of $27, $2 of which went to the bellboy.

I don't think you're following it right. :D

Each salesman paid $9
Total is $27
Bellboy has $2
The salesmen initially paid $10 each, $30 total.
Where's the last dolar gone?
 
There is no reason to add the $2 and $27 – the $2 is contained within the $27 already. Thus the addition is meaningless. Instead the $2 should be subtracted from the $27 to get the revised bill of $25.

This becomes clearer when the initial and net payments are written as simple equations. The first equation shows what happened to the initial payment of $30:

$30 (initial payment) = $25 (to clerk) + $2 (to bellhop) +$3 (refund)
The second equation shows the net payment after the refund is applied (subtracted from both sides):

$27 (net payment) = $25 (to clerk) + $2 (to bellhop)
Both equations make sense, with equal totals on either side of the equal sign. The correct way to get the bellhop's $2 and the guests $27 on the same side of the equal sign ("The bellhop has $2, and the guests paid $27, how does that add up?") is to subtract, not add:

$27 (final payment) - $2 (to bellhop) = $25 (to clerk)

Somebody in that room needs to go ask the desk clerk whats up,.. then go find and kick the bellhops a** :)
 
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