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Math Help - Interesting question

  1. #1
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    Interesting question

    Suppose 150 people joined 3 different communities in Google+. The communities are for 1. Mathematics, 2. Hot Peppers and 3. Cooking

    Here is what is known:

    1. 90 joined Mathematics community
    2. 50 joined Hot Peppers community
    3. 70 joined Cooking community
    4. 15 joined Mathematics and Cooking both
    5. 12 joined Hot Peppers and Cooking
    6. 10 joined all three communities.

    The question is how many joined Mathematics and Hot Peppers (both my favorite) communities.


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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Re: Interesting question

    Hello, saunak!

    Suppose 150 people joined 3 different communities in Google+.
    The communities are: Mathematics, Hot Peppers and Cooking.

    Here is what is known:

    1. 90 joined Mathematics community
    2. 50 joined Hot Peppers community
    3. 70 joined Cooking community
    4. 15 joined both Mathematics and Cooking
    5. 12 joined both Hot Peppers and Cooking
    6. 10 joined all three communities.

    How many joined Mathematics and Hot Peppers only?

    Let x = number in Math and Peppers only.
    Fill in the Venn diagram.

    It should look like this . . .

    Code:
                  o o o           o o o
              o           o   o           o
            o     Math      o    Peppers    o
           o               o o               o
                            x
          o    75-x       o   o    38-x       o
          o               o o o               o
          o           o   o   o   o           o
                    o      10       o
           o       o       o o       o       o
            o         5     o     2         o
              o   o       o   o       o   o
                  o o o           o o o
                  o                   o
                            53
                   o                 o
                    o    Cooking    o
                      o           o
                          o o o
    The total of the numbers is 150.

    (75-x) + x + (38-x) + 5 + 10 + 2 + 53 \:=\:150

    . . . . . . -x + 183 \:=\:150

    Therefore: . x \:=\:33
    Thanks from topsquark
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