SOLUTION: PLEASE HELP ASAP !! During a midnight showing of �Gone With the Wind�, Tom noticed that there were 46 other people in the theater. He also noticed that all of these other people

Question 1076125: PLEASE HELP ASAP !!
During a midnight showing of �Gone With the Wind�, Tom noticed that there were 46 other people in the theater. He also noticed that all of these other people were either sleeping or wearing hats (or both). He counted 31 people sleeping and 24 wearing hats. How many people who were sleeping were also wearing hats?
Thank you in advance
Answer by ikleyn(52805) (Show Source): You can put this solution on YOUR website!
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PLEASE HELP ASAP !!
During a midnight showing of �Gone With the Wind�, Tom noticed that there were 46 other people in the theater.
He also noticed that all of these other people were either sleeping or wearing hats (or both).
He counted 31 people sleeping and 24 wearing hats. How many people who were sleeping were also wearing hats?
Thank you in advance
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The number under the question is  31 + 24 - 46 = 9.


(not counting Tom)

It is a consequence of the general theorem:

     If there are two subsets, A and B, in the finite set F, covering the set F such as  F = A U B,

     then  n(F) = n(A) + n(B) - n(A n B).

See the lesson
- Counting elements in sub-sets of a given finite set
in this site.

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