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Math Help - word problem help

  1. #1
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    word problem help

    120 students were asked about skiing. Here are the results of the poll:
    1. Have you skied either cross-country or downhill? Yes: 65 No: 55
    2. If you answered Yes to Question 1, did you ski downhill? Yes: 28 No: 37
    3. If you answered Yes to Question 1, did you ski country-country? Yes: 45 No: 20
    How many students skiied both cross-country and downhill?

    I'm not sure why it is 8?
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  2. #2
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    Quote Originally Posted by mjoshua View Post
    120 students were asked about skiing. Here are the results of the poll:
    1. Have you skied either cross-country or downhill? Yes: 65 No: 55
    2. If you answered Yes to Question 1, did you ski downhill? Yes: 28 No: 37
    3. If you answered Yes to Question 1, did you ski country-country? Yes: 45 No: 20
    How many students skiied both cross-country and downhill?

    I'm not sure why it is 8?
    Use a Venn-diagram.
    Attached Thumbnails Attached Thumbnails word problem help-skiing.png  
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  3. #3
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    I'm still kinda of lost why we use those values in the circles..
    Last edited by mjoshua; March 31st 2011 at 10:52 AM.
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  4. #4
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    I still don't see why
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by mjoshua View Post
    I still don't see why
    Hi mjoshua,

    That's the beauty of Venn diagrams. They tell the story visually.

    You have a total of 65 people who have skied.

    28 of them have skied downhill and 45 of them have skied cross-country.

    Whoops! That's a total of 73 people. We only had 65 to start with.

    Must be an overlap of 8 people who skied both downhill AND cross-country!

    The intersection of the two circles indicates this overlap.

    Put an 8 in there and make sure the two whole circles add up to 28 and 45, respectively.
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  6. #6
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    Thanks masters that helped! Just curious though, the "Group Forumla" is kinda the same way right? How would you prove that: Total = Group 1 + Group 2 + Neither - Both is true using a venn diagram/same logic? (These are also common word problems that involve only 2 groups)
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