Question 991498
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Saying that 31 speak French doesn't mean that 31 speak only French, some of those 31 may speak Spanish as well.  Likewise some of the 23 who speak Spanish may speak French as well.  Hence, if you just add 31 and 23, you end up counting the people who speak both languages twice.  If there are a total of 60 and 14 speak neither language, then 60 minus 14, or 46 speak either one language, the other language, or both.  But if you add 31 plus 23, you get 54.  54 minus 46 is 8, and so 8 must be the number that are counted twice and that is the number that speak both languages.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

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