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.
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?
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!
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?
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.