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Math Help - Word Problem

  1. #1
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    Word Problem

    At Bison High School, there are 16 students in English Club,
    16 students in Science Club and 20 students in Math Club.
    Of these students, there are 5 students in both the English and
    Science Clubs; 6 students in both the Science and Math
    Clubs; and 8 in both the English and Math Clubs. If only 2
    students are in all three clubs, how many students are in at
    least one of the clubs?
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  2. #2
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    Quote Originally Posted by MATNTRNG View Post
    At Bison High School, there are 16 students in English Club,
    16 students in Science Club and 20 students in Math Club.
    Of these students, there are 5 students in both the English and
    Science Clubs; 6 students in both the Science and Math
    Clubs; and 8 in both the English and Math Clubs. If only 2
    students are in all three clubs, how many students are in at
    least one of the clubs?
    are you familiar with Venn diagrams?
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  3. #3
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    i am but i still cannot put this one together
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  4. #4
    Member oldguynewstudent's Avatar
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    Quote Originally Posted by MATNTRNG View Post
    i am but i still cannot put this one together
    Let e = english only; m = math only; s = science only

    Let x be number in english and science but not math

    Let y be english and math but not science

    Let z be science and math but not english

    x+2= 5 so x = 3

    z+2= 6 so z=4

    y+2 = 8 so y = 6

    16=x+y+2+e

    20=y+z+2+m

    16=x+z+2+s

    Can you figure out the rest from here?
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  5. #5
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    Quote Originally Posted by MATNTRNG View Post
    i am but i still cannot put this one together
    start with the 2 students in all three clubs and work inside out ...
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