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Math Help - set Theory

  1. #1
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    set Theory

    In a survey of 1000 customers, the number of people who used various types of tea leaves were found to be as follows.

    A type only 150, A and C type 90

    A type but not B 210, C type 360

    A type 240, B and C type 100

    None 340

    Find

    (i) How many buy "C" type only

    (ii) How many buy A and B types

    (iii) Number of people buying B and C type but not A type ?

    (iV) How many buy "B" type only ?


    Please solve the problem and show the steps

    thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by pmmeeran View Post
    In a survey of 1000 customers, the number of people who used various types of tea leaves were found to be as follows.

    A type only 150, A and C type 90

    A type but not B 210, C type 360

    A type 240, B and C type 100

    None 340

    Find

    (i) How many buy "C" type only

    (ii) How many buy A and B types

    (iii) Number of people buying B and C type but not A type ?

    (iV) How many buy "B" type only ?


    Please solve the problem and show the steps

    thanks
    start by drawing a Venn diagram. see below.

    fill in the numbers as the problem directs. can you do that?

    if you can do that, can you then answer the questions?
    Attached Thumbnails Attached Thumbnails set Theory-venn-diagram.png  
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  3. #3
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    Quote Originally Posted by pmmeeran View Post
    In a survey of 1000 customers, the number of people who used various types of tea leaves were found to be as follows.

    A type only 150, A and C type 90

    A type but not B 210, C type 360

    A type 240, B and C type 100

    None 340

    Find

    (i) How many buy "C" type only

    (ii) How many buy A and B types

    (iii) Number of people buying B and C type but not A type ?

    (iV) How many buy "B" type only ?


    Please solve the problem and show the steps

    thanks

    see the attached Venn dig.
    from the given condition we have following 7 equations

    a=150
    f+g=90
    a+f=210
    d+e+f+g=360
    a+b+f+g=240
    g+d=100
    a+b+c+d+e+f+g=1000-340

    now there are 7 unknowns and 7 equations
    solve them to find the value of a,b,c,d,e,f,g

    answer for 1) buy "C" type only=e
    2)A and B types=b+g
    3) B and C type but not A type=d
    4)B" type only=c
    Attached Thumbnails Attached Thumbnails set Theory-untitled3.jpg  
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  4. #4
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    Quote Originally Posted by sumit2009 View Post
    see the attached Venn dig.
    from the given condition we have following 7 equations

    a=150
    f+g=90
    a+f=210
    d+e+f+g=360
    a+b+f+g=240
    g+d=100
    a+b+c+d+e+f+g=1000-340

    now there are 7 unknowns and 7 equations
    solve them to find the value of a,b,c,d,e,f,g

    answer for 1) buy "C" type only=e
    2)A and B types=b+g
    3) B and C type but not A type=d
    4)B" type only=c

    try doing this..
    A type only=a=150
    A and C type= f+g=90
    A but not B=a+f=210
    C type =d+e+f+g=360
    A =a+b+f+g=240
    B and C=g+d=100
    none=h=340

    then we have the value of a=150, try subtracting a from "A but not B" that is a+f=210....
    f=210-150
    f=60

    then in the A and C type, that is f+g=90, subtract f to get g..
    f+g=90
    g=90-60
    g=30

    then in the A type, a+b+f+g=240, subtract a, f and g to get b..
    a+b+f+g=240
    b=240-150-30-60
    b=0

    then in the B and C type, g+d=100, subtract g to get d..
    g+d=100
    d=100-30
    d=70

    then in the C type.. d+e+f+g=360, subtract d, f and g from 360 to get e..
    d+e+f+g=360
    e=360 -70- 60-30
    e=360-150
    e=200

    none=h=340

    then we have:
    a=150
    b=0
    c=?
    d=70
    e=200
    f=60
    g=30
    h=340

    add the following and subtract from 1000.
    1000=a+b+c+d+e+f+g+h
    c=1000-850
    c=150

    answer for 1) buy "C" type only=e = 200
    2)A and B types=b+g =30
    3) B and C type but not A type=d =70
    4)B" type only=c =150


    i think that's all.
    Last edited by princess_21; January 20th 2009 at 11:29 PM.
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  5. #5
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    Thank you very much Princes 21 and Sumit 2009
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  6. #6
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    Quote Originally Posted by pmmeeran View Post
    Thank you very much Princes 21 and Sumit 2009
    no thanks for Jhevon?
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  7. #7
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    Thanks for all
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