Results 1 to 7 of 7
Like Tree3Thanks
  • 1 Post By Archie Meade
  • 2 Post By Archie Meade

Thread: Help with venn diagrams/sets word problem

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    22

    Help with venn diagrams/sets word problem

    A survey of 225 adults found that during the last year, 45 traveled by plane but not by train, 70 traveled by train but not by plane, 20 traveled by bus but not by plane or by train, 45 traveled by bus and plane, 20 traveled by all three, and 165 traveled by plane or train. How many did not travel by any of these modes of transportation?

    I'm a little confused here, I tried mapping it out in a venn diagram but it got pretty messy. The wording is a little confusing. Can someone help me solve this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    Quote Originally Posted by zweevu View Post
    A survey of 225 adults found that during the last year, 45 traveled by plane but not by train, 70 traveled by train but not by plane, 20 traveled by bus but not by plane or by train, 45 traveled by bus and plane, 20 traveled by all three, and 165 traveled by plane or train. How many did not travel by any of these modes of transportation?

    I'm a little confused here, I tried mapping it out in a venn diagram but it got pretty messy. The wording is a little confusing. Can someone help me solve this?
    if you draw your Venn diagram with T=train, P=plane, B=bus

    $\displaystyle T\cap P\cap B=20$

    $\displaystyle B\ less\ (T\cup P)=20$

    $\displaystyle (P\cap B)\ less\ T=25$

    $\displaystyle P\ less\ (T\cup B)=20$

    Label the other 3 subsets X=T only, Y=(T Union B) less P, Z=(P Union T) less B

    Then X+Y=70
    165=20+20+25+X+Y+Z=65+X+Y+Z

    100=X+Y+Z

    Then Z=30 and the others follow.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    First step is to place 20 in the intersection of all three.

    Next, 20 travelled by bus, but not by plane or train.
    Place 20 in the bus only subset.

    Next, 45 travelled by bus and plane is the intersection of "b" and "p".
    This consists of two subsets. The first is the intersection of all three,
    the second is the intersection of "b" and "p" that excludes "t".

    Therefore $\displaystyle (p\cap b)\ without\ t=45-20=25$

    Next, 45 travelled by plane but not by train.
    This means we can find the number who travelled only by plane,
    since we have the numbers who used all 3 modes of travel
    and we also have the number who travelled by "bus and plane" only.

    Therefore $\displaystyle p\ without\ t=45$

    $\displaystyle p\ without\ (t\cup b)=45-25=20$

    Four subsets have been filled in.
    The others can be labelled X, Y, Z.

    In finding Z, use the two clues

    $\displaystyle X+Y=70$

    $\displaystyle 20+20+25+X+Y+Z=165$

    Hence, this gives $\displaystyle Z=30$

    X and Y do not need to be found, since we have their sum.

    Finally,

    $\displaystyle 225-(X+Y+Z+20+20+20+25)=225-(70+30+20+20+20+25)=225-185=40$
    Attached Thumbnails Attached Thumbnails Help with venn diagrams/sets word problem-venn.jpg  
    Thanks from Alexnemp and topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2016
    From
    San Diego, California
    Posts
    10

    Re: Help with venn diagrams/sets word problem

    I have an almost exactly similar problem that is "A survey of 245 adults found that during the last year, 70 traveled by plane but not by train, 70 traveled by train but not by plane, 25 traveled by bus but not by plane or by train, 55 traveled by bus and plane, 30 traveled by all three, and 195 traveled by plane or train. How many did not travel by any of these modes of transportation?". I continually come out to the answer 20 but it says it is wrong. Can anyone show me what I may be doing wrong please?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2016
    From
    San Diego, California
    Posts
    10

    Re: Help with venn diagrams/sets word problem

    This is due sunday so any help before then is really appreciated
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    May 2009
    Posts
    612
    Thanks
    309

    Re: Help with venn diagrams/sets word problem

    I get 25 as the answer. Can you show us how you got your answer, please?


    01
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2016
    From
    San Diego, California
    Posts
    10

    Re: Help with venn diagrams/sets word problem

    I figured it out thank you. I kept on getting it wrong because I was not using the correct 3 values when determining z. Thank you for your help anyways!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Venn Diagrams
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Oct 4th 2011, 09:12 AM
  2. Venn Diagrams
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Dec 12th 2010, 01:14 PM
  3. Venn Diagrams
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Apr 23rd 2010, 07:35 AM
  4. Venn Diagrams
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Jun 24th 2008, 10:09 AM
  5. Simple Word Problem Sets, Venn
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Jan 12th 2007, 01:52 PM

Search tags for this page

a survey of 160 householders all of whom kept a television or radio or both showed that 85 kept televisions and 75 kept radios .how many kept both venn diagram
,

venn diagram of travel by bus and travel by train

,

Out of 95 travelers interviewed, 7 travelled by bus and train only, 3 by train and car only, 8 travelled by all three means of transport. The number,x, of travelers who travelled by bus only was equal to the number who travelled by bus and car only.

,

out of 95 travelers intervi, 7 travelled by bus and train only, 3 by train and car only, 8 travelled by all three means of transport using set and venn diagrams

,

Out of 95 travellers interviewed,7 travelled by bus and train only,3 by train and car only and 8 travelled by all the three means of transport. The number x of travellers who travelled by bus only is equal to the number who travelled by bus and car only.

,

OUT OF 4O TRAVELLERS 12 HAVE TRAVELLED TO ACCRA BUT NOT LONDON 8 TRAVELLED TO LONDON BUT NOT ACCRA 1O CLAIMED THEY HAD NEVER TRAVELLED TO EITHER CITY USING VENN DIAGRAM FIND THE NO. OF TRAVELLERS THAT HAD TRAVELLED TO BOTH CITIES DOES NEVER TRAVELLED TO A

,

out of 95 travellers interviewed , 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all three means of transport. The number, x , of travellers who travelled by bus only was equal to the number who travelled by bus and car onl

,

out of 95 travellers interviewed , 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all three means of transport. The number, x , of travellers who travelled by bus only was equal to the number who travelled by bus and car onl

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum