Maths

In a class of 80 students 53 study art,60 study biology,36 study art and biology,34 study art and chemistry,6 study biology only and 18 study biology but not chemistry.Illustrate the information on a Venn diagram.Determine the number of student study (i)art only (ii)chemistry.

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  1. Make the Venn diagram. Let
    a = # who study art only
    b = # who study biology only
    c = # who study chemistry only
    x = # who study only art and biology
    y = # who study only art and chemistry
    z = # who study only biology and chemistry
    n = # who study all three subjects
    Now, we know that
    a+x+y+n = 53
    b+x+z+n = 60
    x+n = 36
    y+n = 34
    b = 6
    b+x = 18
    Solving that, we get
    a = 7
    Note that nowhere does c get used. So, since the sum of all the other numbers is 77, if we assume that all 83 students study something, then 6 study only chemistry.

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    oobleck

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