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Math Help - A question I have been stuck on for a while....

  1. #1
    M23
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    A question I have been stuck on for a while....

    Each member of a neighbourhood athletics club plays at least one of the following sports: basketball, soccer, or hockey. In the club, 25 members play basketball, 12 play basketball and soccer, 10 play basketball and hockey, 9 play soccer and hockey, 37 play basketball or soccer, 42 play soccer or hockey, and 4 play all three sports. How many members are in the club? A. 47 B. 48 C. 49 D. 50 Help would be very much appreciated!
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  2. #2
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    I'm getting 49. You'll have to draw a Venn diagram with three circles. When you're done, you'll find that:

    7 play basketball only,
    7 play soccer only,
    12 play hockey only,
    8 play basketball and soccer and not hockey,
    5 play soccer and hockey and not basketball,
    6 play basketball and hockey and not soccer,
    4 play all three.

    Total: 49

    You state that 25 play basketball. If you add all the numbers that involve basketball:
    7 play basketball only,
    8 play basketball and soccer and not hockey,
    6 play basketball and hockey and not soccer,
    4 play all three,
    you get 25. You can repeat for the other conditions to verify.

    Sorry this is not that helpful. I don't have a camera handy to take a picture of my Venn diagram.


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  3. #3
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    Quote Originally Posted by M23 View Post
    Each member of a neighbourhood athletics club plays at least one of the following sports: basketball, soccer, or hockey. In the club,
    25 members play basketball,
    12 play basketball and soccer,
    10 play basketball and hockey,
    9 play soccer and hockey,
    37 play basketball or soccer,
    42 play soccer or hockey, and
    4 play all three sports. ......<<<<< first value to put in.
    How many members are in the club? A. 47 B. 48 C. 49 D. 50 Help would be very much appreciated!
    Draw a Venn diagram. Put in the given values. Start with the central value (=intercept of all three areas).

    See attachment
    Attached Thumbnails Attached Thumbnails A question I have been stuck on for a while....-clubmembers.png  
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  4. #4
    M23
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    Thank you very much.
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