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Article #11482

Re: THE MISSING DOLLAR!

#11482
From: Fred Kochman
Date: Thu, 30 Nov 1995 00:00
47 lines
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In article <49ka9b$6ij@metro.ucc.su.OZ.AU> Andrew Laming <alaming@extro.ucc.su.oz.au> writes:

   This problem is driving me crazy. If you can solve and explain it to me 
   I would be very grateful.

   Three men walk into a store and buy a $30 radio. 
   They each put in $10, making $30. 
   The shopkeeper later realises that the radio was on sale for $25. 
   The shopkeeper is a crook and instead of dividing the $5 between the 
   three men he pockets $2 and gives each man $1 back. 
   So in fact each of the three men paid $9 each which makes $27 and the 
   shopkeeper keeps $2. 
   Now $27 + $2 = $29. 
   What happened to the extra dollar?


   I have no problem understanding that the radio actually cost $25 so each 
   man paid 
   25 � 3 = $8 1/3 dollars. 
   Now,
   $8 1/3 * 3 = $25. 
   Plus $3 back is $28, 
   plus the $2 the shopkeeper kept makes $30.

   I don't understand where the error is in saying that each man paid $9 
   and the shopkeeper kept $2 which makes $29. There is obviously an error 
   but I can't see it. 

   If you can explain it to me I would be eternally grateful as it is 
   driving me crazy. 

   Thanks, 

   Andy.

Andy, the three men paid $30 and then got $3 back, so they actually
paid only $27.  But if you then add the $2 kept by the shopkeeper,
bringing the total up to $29, you are counting those $2 _twice_,
as they were already included in the $30 which the shopkeeper
was given in the first place.

Giving the shopkeeper $30 was a transfer of money.
Giving back $3 was a transfer of money.
But for the shopkeeper to retain $2 which he already has
and put it in his pocket, is not a transfer of money.
So it doesn't make sense to add the $2 to the $27, as if
it were an additional sum remitted to the shopkeeper.
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From: kochman@harder.ccr-p.ida.org (Fred Kochman)
Subject: Re: THE MISSING DOLLAR!
Date: 1995/11/30
Message-ID: <KOCHMAN.95Nov30161926@harder.ccr-p.ida.org>
X-Deja-AN: 120576866
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references: <49ka9b$6ij@metro.ucc.su.OZ.AU>
organization: IDA Center for Communications Research
newsgroups: aus.mathematics