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May 13th, 2009, 01:58 PM   #1
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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.
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May 13th, 2009, 04:13 PM   #2
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What progress have you made, and what have you assumed? There are different solutions, depending on what you assume.
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May 13th, 2009, 04:23 PM   #3
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Re: algebra 4 word problem

What matters is that 35% suffer from heart disease and of those 25% are unfit, and so constitute that section of the unfit population. See the diagram below, and see if you can express that algebraically. The rest suffer from something else,but we are not asked to determine that.

[attachment=0:3gx1vi0f]Percent.jpg[/attachment:3gx1vi0f]
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May 13th, 2009, 05:19 PM   #4
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Quote:
Originally Posted by Dave
. . . and of those 25% are unfit, . . .
That's not what the question stated, which was that 25% of heart disease is caused by being unfit. They're not the same.
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May 14th, 2009, 07:53 AM   #5
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Re: algebra 4 word problem

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.[attachment=0:1alx2sjk]venn.gif[/attachment:1alx2sjk]

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?
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May 14th, 2009, 09:00 AM   #6
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Whether it's possible depends on what assumptions you make. You have made assumptions in producing your diagram, and further assumptions in stating "14 unfit w/HD divided by 35 total with HD = 40% HD due to unfitness". Consider carefully the phrase "due to unfitness"; it is quite possible to have unfitness that is due to heart disease, rather than the other way round.
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May 14th, 2009, 09:36 AM   #7
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Re: algebra 4 word problem

Not entirely sure what you mean by 'assumptions'; as far as I can see, I haven't made any. The Venn Diagram uses the 'givens' in the original word problem: 35% have HD (65% don't), and 40% are unfit (60% are fit).

As for what is meant by 'unfitness', it means they don't exercise or engage in other regular physical activity. It's not possible that lack of activity is due to heart disease (unless you're talking about bed-ridden patients who can't exercise, which I'm not).
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May 14th, 2009, 10:03 AM   #8
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The problem stated that 40% of the population is unfit, but you assumed you could apply 40% separately to those with and those without heart disease, which doesn't follow. Your assumptions that bed-ridden patients are excluded and that those who don't exercise regularly are bed-ridden (which seems absurd to me) couldn't possibly be deduced from the original wording. Even if you know they are correct, you are further assuming that when an unfit patient has heart disease, their unfitness was a cause of the heart disease, which doesn't follow, since their unfitness may have started after they already had heart disease and be caused by something unrelated to the heart disease, such as depression or laziness.
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May 14th, 2009, 11:22 AM   #9
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Re:

Quote:
Originally Posted by skipjack
Quote:
Originally Posted by Dave
. . . and of those 25% are unfit, . . .
That's not what the question stated, which was that 25% of heart disease is caused by being unfit. They're not the same.
Semantics. "25% of heart disease is due to being unfit," More completely, perhaps... "of those [with heart disease] 25% [is due to being] unfit" ? The rest is due to other causes.
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May 14th, 2009, 12:16 PM   #10
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Re: algebra 4 word problem

Okay, I solved this using the modified Venn Diagram below.

Thanks for your input, Skipjack. I wasn't 'assuming' that I could apply the 40% unfit pop. equally to all heart disease patients; I merely hadn't figured out how to account for the 25% differential in heart disease (HD) among the fit and unfit. You're right -- they're not going to be the same. The Venn Diagram below is more accurate, showing that HD is higher among the unfit.

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.

Sorry I wasn't clear about the meaning of the 25%. You got it right, Skipjack: Of those with heart disease, 25% is due to being unfit. The rest is due to other causes.

Thanks for everyone's help.
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