Venn Diagram question..?

A record of 959 high school graduates were examined, and the following information was obtained: 417 took biology, and 413 took geometry. If 247 of those who took geometry did not take biology, how many graduates took the following?

How would I find out the number of students who took at least one of the classes, and both classes from that information?

3 Answers

  • Anonymous
    1 decade ago
    Favorite Answer

    Let G be the set which contains all geometry students.

    Let B be the set which contains all biology students.

    (2) Since 413 students did take geometry, and of those, 247 did not take biology, then the number left of the 413 is the number who took both.

    413 - 247 = 166 took both courses. <<<<<

    For a Venn diagram this would be A intersect B.

    1) We can now look at B and not G

    The ones who took biology (417) and did not take geometry is:

    417 - 166 = 251 = B and not G

    The set G and not B was given - it has 247 students.

    The following three sets do not intersect one another.

    a) G and not B has 247 students (or elements)

    b) G and B has 166 students (elements)

    c) B and not G has 251 students (elements)

    Since none of these sets intersect each other, their union has

    251 + 166 + 247 = 664 (<<<<<) students and those are the number who took at least one class.

    For your Venn diagram the following should help:

    This is the union of (B and G) with (B and not G) and with (G and not B)

    Answers: <<<<<

    166 took both courses.

    664 took at least one course.

  • Anonymous
    1 decade ago

    Since 247 of the 413 who took geometry did NOT take biology

    that implies that (413 - 247) = 166 took both Geometry and Biology.

    Which means (417 - 166) = 251 took only Biology.

    Also, [959- (247 + 166+ 251)] = 295 did not take either of the classes.

    Therefore the number of students who've taken atleast one class is (247 + 166+ 251) = 664

  • Anonymous
    1 decade ago

    number of students who took at least one of the classes 830

    both classes 247

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