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This question already has an answer here:

Three friends brought 3 pens together each 10 dollars. Next day they got 5 dollars cash back so they shared each 1 dollar and donated 2 dollars. Now the pen cost for each guy will be 9 dollars (\$10 -\$1).

But if you add all 9+9+9 = 27 dollars and donated amount is 2 dollars so total 29 dollars.

Where is the other \$1?

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marked as duplicate by user642796 Sep 4 '13 at 13:07

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Can it really be that we have nothing do close this as an exact duplicate of? Closing as "off topic" seems definitely wrong to me; the question of which calculations are the right ones to perform in a given (imagined) real-world situation shouldn't be off topic. We can call it a question about mathematical modeling if we want to be highbrow about it. $\endgroup$ – Henning Makholm Aug 30 '13 at 21:46
  • $\begingroup$ I upvoted the question to make up for a downvote. Questions far stupider are asked here all the time and many receive lengthy answers. $\endgroup$ – Stefan Smith Aug 30 '13 at 22:53
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    $\begingroup$ @Henning, it's actually a nice example of a fallacy in mathematics (like the 1=2 equation where one divides by zero). Do you agree in creating a "fallacy" tag (and tagging this question as such)? $\endgroup$ – JMCF125 Aug 30 '13 at 22:56
  • $\begingroup$ @Gerry, probably, Wikipedia agrees. As you contributed to close, couldn't you either merge these or change the reason for the close? $\endgroup$ – JMCF125 Aug 31 '13 at 20:52
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    $\begingroup$ I temporarily re-opened this question to close.. errr.. mark it as a duplicate. No reopen votes were left orphaned by my actions. IMO (and that of others, it seems) being a duplicate is more of an issue for this question. $\endgroup$ – user642796 Sep 4 '13 at 13:10
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The last conclusion is simply wrong. You are right, they paid $27$ dollars altogether. The pens however cost $25$ dollars ($30$ dollars initially, then $5$ discount), so that's the two dollar donation difference.

There is no sense in adding the $2$ dollars, since the nine dollars each friend spent includes the donation.

EDIT: As T. Bongers noted, this is a known fallacy, so you might want to check Wikipedia or google for "missing dollar" for more detailed explanations.

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  • $\begingroup$ I know actual coat is 25 dollars but when you calculate reverse we are only get 29 dollars $\endgroup$ – Jag Aug 30 '13 at 21:03
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    $\begingroup$ As I stated, the reverse calculation is wrong. Since the pens cost $25$ dollars, but the friends spent $27$ dollars, this $27$ dollars include the donation, so subtract it, don't add it. Actually, the $30$ dollars are of no relevance, as only $27$ were used. They could even be billionaires... $\endgroup$ – Tomas Aug 30 '13 at 21:05
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    $\begingroup$ There is no missing dollar... $\endgroup$ – user61527 Aug 30 '13 at 21:15
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    $\begingroup$ Hehe, nice! I did not know that this was that popular, but it's even on - @JAG, check for reference - Wikipedia. $\endgroup$ – Tomas Aug 30 '13 at 21:18
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10 x 3 = 30. 30 - 5 = 25. 25 + 3 = 28. 28 + 2 = 30. so, no missing $.

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