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Topic: Missing dollar
Replies: 0

 Ted Alper Posts: 118 Registered: 12/6/04
Missing dollar
Posted: Oct 11, 2000 2:26 AM

if you look in the archives for this discussion group at
www.forum.swarthmore.edu
you can see the "missing dollar" problem discussed back in March
of '95.

Unfortunately, I can't seem to find my post on the subject at
the time... but it suggested changing the values in the problem to make
clear the error in reasoning... for example, if they were originally
told the room cost \$300, then they'd each pay \$100... and if
the room really cost just \$25, and the bellboy was given \$275 to
return to them, but decided to pocket \$272 of it and
give each man just one dollar, the pattern of the problem would be:
each man paid \$99 (for a total of \$297) and the bellboy kept \$272.

Would you say -- that sums to 569, where did the extra \$269 come
from? You are counting the \$272 twice, once as part of the
money spent by the men and once as part of the money pocketed by the
bellboy.

It's more correct to say: the men have spent a total of \$297, of which
\$25 went to the hotel and \$272 was stolen by the bellboy. If you want
to account for the original \$300, you add the three dollars the men
received back to the \$297 they spent.

In the same way, in the original problem, the men spent a total of
\$27, of which \$25 went to the hotel and \$2 to the bellboy. If you
want to account for the original \$30, you add the three dollars they
received back to the \$27 they spent.

Ted Alper

P.S. I'm enjoying rereading the archives of this group from the
mid-1990s... it's amazing how little has changed!