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Math Help - Venn Diagram

  1. #1
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    Venn Diagram

    I need help with a Venn Diagram question. Oridnarily I know you would start in the middle but that is the piece that is missing in this problem. Can you please provide a formula to work this problem?

    A recent survey of 150 people showed the following investments in stocks bonds and CODs

    111 people invested in stocks
    98 people invested in bonds
    100 people invested in CODs
    80 people invested in stocks and bonds
    83 people invested in bonds and CODs
    85 people invested in stocks and CODs
    9 people did not invest in any of the three

    How many people invested in all three
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  2. #2
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    Call the middle intersection X,
    and you will the the following picture.
    Since the universal set over here is 150,
    we add each one and get,
    \begin{array}{c}<br />
x-64\\<br />
x-65\\<br />
x-68\\<br />
80-x\\<br />
85-x\\<br />
83-x\\<br />
\underline{x+9}\\<br />
x+60
    Thus,
    x+60=150
    Thus,
    x=90
    Attached Thumbnails Attached Thumbnails Venn Diagram-picture10.gif  
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  3. #3
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    Venn Diagram

    Where did you get the
    x-64
    x-65
    x-68?

    The total value for stocks should be 111, for bonds 98 and for cods 100. If x was 90 you would be over.

    Thanks!
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  4. #4
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    Quote Originally Posted by gogo08
    Where did you get the
    x-64
    x-65
    x-68?

    The total value for stocks should be 111, for bonds 98 and for cods 100. If x was 90 you would be over.

    Thanks!
    Because those extreme outside circle parts are,
    111-(x+[80-x]+[85-x])=x-64
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  5. #5
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    Quote Originally Posted by ThePerfectHacker
    Because those extreme outside circle parts are,
    111-(x+[80-x]+[85-x])=x-64
    Hello,

    that's what I've got:

    111-(x+[80-x]+[85-x])=x-54

    That'll give as the final result x = 70 which fits a little bit better because with your result it could happen that -10 people buy bonds and stocks.

    Greetings

    EB
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  6. #6
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    Quote Originally Posted by earboth
    Hello,

    that's what I've got:

    111-(x+[80-x]+[85-x])=x-54

    That'll give as the final result x = 70 which fits a little bit better because with your result it could happen that -10 people buy bonds and stocks.

    Greetings

    EB
    I hate these types of mistakes.
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