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Math Help - Set Problems

  1. #1
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    Set Problems

    Ok, I've done these types of problems before, but now I'm not given an intersections. Here is the problem:

    At a school fair 34 students are given awards for projects. 14 awards were given for biology, 13 in chemistry and 21 in physics. If 3 students are given awards in all three subject areas how many awards are received for one subject area and and 2 subject areas?

    So here is what I've started on...



    I just don't know where to go without the intersections I guess? Help on this would be much appreciated!
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  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
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    Quote Originally Posted by intervade View Post
    Ok, I've done these types of problems before, but now I'm not given an intersections. Here is the problem:

    At a school fair 34 students are given awards for projects. 14 awards were given for biology, 13 in chemistry and 21 in physics. If 3 students are given awards in all three subject areas how many awards are received for one subject area and and 2 subject areas?

    So here is what I've started on...



    I just don't know where to go without the intersections I guess? Help on this would be much appreciated!
    There were 34 students awarded prizes. 3 of these recieved a prize in each subject, leaving 31 students to split the rest.

    Personally, I would stick this all into a formula (well, actually, two formulas),

    n students got 1 prize,

    m students got 2 prizes, so

    Note that n+m = 34-3=31, and that n+2m = (13-3) + (21-3) + (14-3) = 39. Solve.

    Do you understand where I got these two equations from? The first is just counting the number of students, the second the number of awards.
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