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Apple Paradox

Date: 03/07/2002 at 00:11:50
From: Milosch
Subject: Trick Question

Ms. G and Mr. S each bring 30 apples to sell at the market. 
Ms. G sells her apples at $1 for 2 apples and makes $15. 
Mr. S sells his apples at $1 for 3 apples and makes $10. 

Ms. G and Mr. S combine their offer so it equals 5 apples for $2. 
In theory they should make $25 combined, but at the end of the day 
they sell all of their apples but they only make $24.

Date: 03/07/2002 at 00:34:57
From: Doctor Twe
Subject: Re: Trick Question

Hi Milosch - thanks for writing to Dr. Math.

Here's one way to explain the apparent paradox.

In order for them to combine their offers and sell 5 apples for $2, 
Ms. G must supply 2 of her $.50 apples and Mr. S must supply 3 of his 
$.33 apples for each customer who buys 5 apples.

But Mr. S runs out of $.33 apples after the first 10 customers, while 
Ms. G still has 10 of her $.50 apples left. So to continue offering 
the combined special, Ms. G has to "mark down" 6 of her remaining 10 
apples to Mr. S's $.33 price. She loses $.17 per apple on these marked 
down apples, accounting for the "missing" dollar.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum   
Associated Topics:
Middle School Puzzles

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