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 Subj:.....Monocles And Glasses (S672)           From: MathNexus.wwu.edu           on 11/28/2009 Drawing from Millan.net...

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Source: http://mathnexus.wwu.edu/Archive/problem/detail.asp?ID=131

In a small village known as Spectropolis, every person
wears corrective lenses (monocles or glasses) that are
either clear or tinted.

Half the people wear monocles and half of the remaining
people do not wear tinted lenses.

Also, half of the monocle wearers do not wear tinted lenses.

If eighteen tinted lenses are enough to exactly supply the
needs of the people in Spectropolis, what is the village's
population?

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 Drawing from tom on 8/21/2009
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Note: Try to draw a picture to represent both the full
situation and the individual clues.  Also, will guess-
and-check work?

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 Finger pointing down from darrell94590 on 1/2/2006
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 From: lubin100@ on 4/2/2009
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THE SOLUTION

Solution Commentary: Rather than a solution, some more questions:

 What fraction of the population wears tinted lenses?
 What fraction of the population wears tinted monocles?
 Why is 3 a magical number in this problem?

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 Drawing from tom on 8/21/2009
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My Solution: Let P = total population
..............then ¼ P = population with tinted monocles
...............and ¼ P = population with tinted glasses

Total lenses = population with tinted monocles
...............plus 2 X population with tinted glasses

..........18 = ¼ P + 2 ( ¼ P )
..........18 = ¾ P
..........24 =   P

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