Results 1 to 8 of 8

Math Help - algebra 4 word problem

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    5

    algebra 4 word problem

    Hello,

    What equation would I use to solve the following:

    If 40% of the population is unfit, and
    35% of the population has heart disease, and
    25% of heart disease is due to being unfit,

    what is the percent of the population that is both unfit and has heart disease?

    Please include the equation you use to get your answer.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by sssmath View Post
    Hello,

    What equation would I use to solve the following:

    If 40% of the population is unfit, and
    35% of the population has heart disease, and
    25% of heart disease is due to being unfit,

    what is the percent of the population that is both unfit and has heart disease?

    Please include the equation you use to get your answer.

    Thanks.
    Use P (A\cup B) = P(A) + P(B) - P(A \cup B)

    This can be explained clearly with a Venn diagram
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2009
    Posts
    5
    ouch...you've exceeded my level of math knowledge; maybe if you filled in the numbers for the variables I could follow what you mean.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by sssmath View Post
    ouch...you've exceeded my level of math knowledge; maybe if you filled in the numbers for the variables I could follow what you mean.
    Actually, I'm not too sure, I may have misread it - I used a probability formula but I'm not sure if it's right now
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2009
    Posts
    5
    I did a quick lookup on Venn Diagrams; I see your point.

    The appropriate Venn Diagram would be a square divided into 4 quarters by a horizontal line intersecting a vertical line. The two top quarters are, say, heart disease patients; the two bottom quarters are non-patients. The two left quarters are fit people; the two right quarters are unfit people.

    But what are the relative percents of the 4 quarters?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2008
    Posts
    8
    hey,
    Start out by labeling outside of each section. Take the information that you know, and work from there. For example, you have 40% of the whole population observed that is unfit. This means that this 40% is split between both heart patients, and non-heart patients. This also means that the percentage of fit people will equal 60%
    The percentage of heart-diseased patients is 35%, which means that the people without is 65%.

    Now that all of the outside percentages are labeled, you can fill in the inside.
    The only information you have to do this is the unfit/heart patient box, which is 25%.
    from this point on, each column and row must equal 100%.

    This is about as far as I can get, I'm not really sure how to set up your equation

    I hope this helps, it's kind of confusing when I can't write it out. Good luck!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2009
    Posts
    5
    I got the following using a 1 x 1 square Venn diagram. The .65 line divides heart disease (HD) patients from non-patients; HD patients are the two squares on the right, taking up 35%, in red. The .6 line divides fit people from unfit ones; fit people are the two top squares, taking up 60%, in yellow. Orange is fit & HD together; white is neither fit nor HD.

    From that, I get the following numbers (by multiplying the dimensions of each quarter, like finding the area of a square):

    fit HD: 60% x 35% = 21%
    unfit HD: 40% x 35% = 14%
    fit, no HD: 60% x 65% = 39%
    unfit, no HD: 40% x 65% = 26%

    That adds up to 100%. The only problem is that the percent of HD due to being unfit doesn't equal 25%. Assuming a population of 100:

    14 unfit w/HD divided by 35 total with HD = 40% HD due to unfitness.

    The reason the 25% isn't represented is that it's not used in any of the four equations. Can anyone think how to integrate it? Or is it possible that the original word problem is logically impossible?
    Attached Thumbnails Attached Thumbnails algebra 4 word problem-venn.gif  
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    May 2009
    Posts
    5
    Okay, I solved this using the modified Venn Diagram below.

    I used simultaneous equations to get x and y. I won't go into detail because it was rather complex, but one equation stated that the area of the added yellow square = that of the added red square, so that the total area remains unchanged. The second equation integrates the 25% differential.

    Thanks for everyone's help.
    Attached Thumbnails Attached Thumbnails algebra 4 word problem-venn2.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Algebra word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 1st 2010, 01:46 PM
  2. algebra word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 16th 2010, 01:05 PM
  3. Algebra word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 14th 2009, 02:54 PM
  4. algebra word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 13th 2009, 10:34 PM
  5. Algebra Word Problem-HELP!
    Posted in the Algebra Forum
    Replies: 8
    Last Post: July 25th 2008, 01:57 AM

Search Tags


/mathhelpforum @mathhelpforum