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In a town there was a population of 660 dogs and cats. Although, many of the dogs and cats were crazy. 25% of the actual dogs thought they were cats, and 20% of the actual cats thought they were dogs.

In a poll regarding whether one is dog or cat, in which every animal of this population participated, 40% answered "cat".

How many dogs respectively cats were there in this population?

Govtcheez

11-13-2002, 01:30 PM

I'm not sure about the math, but I think there's somewhere in the neighborhood of 480 dogs and 170 cats... I'm not sure what happened to the other 10, though. We'll just assume they're rats.

I'm not sure either... but I get

463 dogs: 116 of them think they're cats

197 cats: 40 of them think they're dogs

edit: well, it's wrong... doesn't work out :rolleyes:

kermi3

11-13-2002, 01:57 PM

I do know the math :) and the answer is:

180 Cats

480 Dogs

I can explain the math if somone wants ;)

I'd be delighted if you could explain for us how you got to this conclusion:D

kermi3

11-13-2002, 02:11 PM

Is this for homework? A stats class perhaps?

Basically is this graded? If not I'll explain heh.

tedde

11-13-2002, 02:14 PM

no homework, we had this question on a math test we had yesterday but nobdy didn't make it, and we want the solution..

PJYelton

11-13-2002, 02:21 PM

no problem - make the number of cats be "x", then the number of dogs is "660-x". Now, 40% of 660 said they were cats, which is 264. 80% of the cats say they are cats, 25% of the dogs think they are cats, therefore the equation becomes:

.8*x+.25*(660-x)=264

work the equation, and x=180, so the number of cats is 180, the number of dogs is 480. Sucks to be a cat in this town :D

golfinguy4

11-13-2002, 02:24 PM

.25d + .8c = .4*660

d + c = 660

Solve the system.

Edit: PJ beat me with a different way.

kermi3

11-13-2002, 02:24 PM

Ah ok, well I'm drawing an easy to read explanation....of why it all works:

hk_mp5kpdw

11-13-2002, 02:34 PM

Well...

.75D + .20C = .60 * 660 and

.25D + .80C = .40 * 660

So...

.75D + .20C = 396 and

.25D + .80C = 264

Continuing...

.75D + .20C = 396 and

-.75D - 2.40C = -792

Adding we get...

-2.2C = -396

Dividing we have...

C = 180

Since C+D=660, and C=180, D=480. Did I make any mistakes?

kermi3

11-13-2002, 02:34 PM

Ok then...Here's the answer:

Check out the picture, we know what's in black, red's from my calculations.

Oh I should explain it....

The numbers are the percent of something happenning given what was on the previous branches, so there's a .25 chance that a dog answered cat. And due to the nature of probablilty there is a .727*.25 chance that you will randomly pick a dog that answered cat

Now the total number AC is:

AC=.8c +.2d

.4 * 660 = .8c +.2d

Using d = 660 - c:

.4*660 = .8c + .2(660 - c)

.4*660 = .8c + 165-.25c

Solve it all:

c = .273 - That's the pecent of cats

and of course since c% + d% much = 1; d% = .727

now C%*660=number of cats

and D%*660=number of dogs

and therefore 480 cats and 180 dogs

The other numbers (.454 and .546) I used to check it.

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