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Math Help - Set theory 2

  1. #1
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    Set theory 2

    Could someone please help me how to calcute the anwers of these problems?

    a) A group of 700 tourists are visiting a city and the following information is given:

    379 visited the park
    419 visited the museum
    260 visited the theatre
    102 went to the theatre but didnt go to the park nor the museum
    92 went to the museum but didnt go to the park nor the theatre
    110 went to the park but didnt go to the theatre
    60 went to the three places

    304 tourists went to only place and 287 went to two places. Calculate how these values are obtained.

    b) A car agency sold 180 units during a year with the following characteristics:

    57 were standard
    77 had air conditioning (ac)
    45 were standard and had ac
    10 were standard but didnt have ac or stereo
    28 were standard and had ac, but didnt have stereo
    90 didnt have any of these three
    19 had ac and stereo

    22 units had stereo. Find out how this was obtained.
    Last edited by bret80; July 31st 2006 at 07:42 AM.
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  2. #2
    Eater of Worlds
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    These things can be real 'head-scratchers', can't they?.

    If I did this correctly, here's the Venn diagram. It's kind of lop-sided, but should put forth the idea. It would appear 22 have stereo.
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by bret80
    Thanks for your help, I could spend days solving these problems, so I need a bit more of your aid.

    a) A group of 700 tourists are visiting a city and the following information is given:

    379 visited the park
    419 visited the museum
    260 visited the theatre
    102 went to the theatre but didnt go to the park nor the museum
    92 went to the museum but didnt go to the park nor the theatre
    110 went to the park but didnt go to the theatre
    60 went to the three places

    How many of these tourists assisted to exactly one and two of these places?
    I don't really understand the question, is it how many tourists went to only one place, or two places, or three?
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  4. #4
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    I wrote down the correct answers. I would like to know how these values are obtained. Thanks.
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  5. #5
    Member Glaysher's Avatar
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    Quote Originally Posted by bret80
    Could someone please help me how to calcute the anwers of these problems?

    a) A group of 700 tourists are visiting a city and the following information is given:

    379 visited the park
    419 visited the museum
    260 visited the theatre
    102 went to the theatre but didnt go to the park nor the museum
    92 went to the museum but didnt go to the park nor the theatre
    110 went to the park but didnt go to the theatre
    60 went to the three places

    304 tourists went to only place and 287 went to two places. Calculate how these values are obtained.

    .
    I got a answer that made no sense when I did it this way but got the exact answers when I assumed the 110 line should have read 110 went to the park but didn't go to the theatre nor the museum. Please could you check the question in case I did make a mistake as I am distracted by having my baby son sleep on me!

    In that case 304 = 102 + 92 + 110 for only one

    Exactly two is more difficult to go through here. If I'm right about the question I can send the answer as an attachment. Just tell me what format you would prefer.
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  6. #6
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    Hi Glaysher,

    Thanks for trying the figure out the answers. I assume you're right about the 110 going to neither of those places. I guess excell is fine or word.
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  7. #7
    Member Glaysher's Avatar
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    See attachment. Drawing Venn diagrams in questions like this is often the best way of approaching the problem.
    Attached Files Attached Files
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  8. #8
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    110 went to the park but didnt go to the theatre
    presumable this should have been

    "110 went to the park but didnt go to the theatre nor the museum".

    but anyway Glaysher, you had:

    x+z = 209
    y+z = 267
    x+z = 98
    its much nicer to add all three to get
    2(x+y+z) = 574
    hence x+y+z = 287
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