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Math Help - Percentage problem

  1. #1
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    Percentage problem

    I need help with the following percentage question:


    In a 400-people population, it has been done examinations to diagnose anemia and intestinal parasitism. The results made it clear that:

    - 80% of the people with anemia have also intestinal parasitism;

    - 50% of the people with intestinal parasitism have also anemia;

    - 220 people have neither anemia nor intestinal parasitism.

    Out of the 400 people, what is the percentage of people with anemia?


    I know that the answer is 25%, but how do I get at it?
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  2. #2
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    Quote Originally Posted by nvwxgn View Post
    I need help with the following percentage question:


    In a 400-people population, it has been done examinations to diagnose anemia and intestinal parasitism. The results made it clear that:

    - 80% of the people with anemia have also intestinal parasitism;

    - 50% of the people with intestinal parasitism have also anemia;

    - 220 people have neither anemia nor intestinal parasitism.

    Out of the 400 people, what is the percentage of people with anemia?


    I know that the answer is 25%, but how do I get at it?
    You must start defining.

    A = # of folks with anemia
    P = # of folks with parasites
    B = # of folks with both
    220 = # of folks with neither

    We have immediately:

    1) A + P - B = 400-220 = 180
    2) A(0.80) = B
    3) P(0.50) = B

    Solving - Substitute 2) and 3) into 1)

    (b/(0.8) + B/(0.5) - B) = 180 ==> B = 80

    Back-Substitute into 2)

    A = 80/(0.8) = 100

    Answer: 100/400 = 0.25

    Note: I did not see how to solve this problem until AFTER I wrote clear and sufficient definitions. Only after those four rows did I see where this was going and that the information given was sufficient.

    Note: Notice how I did NOT solve for P. P was not the most convenient first solution (B) and P was not the item asked for (A). Again, the defintions, clear and sufficient, made it possible to know what to go for first.
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  3. #3
    Super Member bigwave's Avatar
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    you can also do this with just one varible

    let A = people with anemia

    since half the people with intestinal parasitism have A and those with A .8 have intestinal parasitism

    then
    <br />
A + .8A = 180
    so A = 100

    and \frac{400}{100} = .25

    I should mention that I also drew a diagram of what was going on... then it all came down to something
    obviously simple. word problems really need to be transformed into a way that is clear what is happening
    Last edited by bigwave; December 5th 2009 at 12:10 AM. Reason: added comment
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  4. #4
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    Good. Thanks a lot
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