Maths problem

• 11-13-2002
Zewu
Maths problem
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?
• 11-13-2002
Govtcheez
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.
• 11-13-2002
BMJ
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:
• 11-13-2002
kermi3
I do know the math :) and the answer is:

180 Cats
480 Dogs

I can explain the math if somone wants ;)
• 11-13-2002
Zewu
I'd be delighted if you could explain for us how you got to this conclusion:D
• 11-13-2002
kermi3
Is this for homework? A stats class perhaps?

Basically is this graded? If not I'll explain heh.
• 11-13-2002
tedde
no homework, we had this question on a math test we had yesterday but nobdy didn't make it, and we want the solution..
• 11-13-2002
PJYelton
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
• 11-13-2002
golfinguy4
.25d + .8c = .4*660
d + c = 660

Solve the system.

Edit: PJ beat me with a different way.
• 11-13-2002
kermi3
Ah ok, well I'm drawing an easy to read explanation....of why it all works:
• 11-13-2002
hk_mp5kpdw
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

-2.2C = -396

Dividing we have...

C = 180

Since C+D=660, and C=180, D=480. Did I make any mistakes?
• 11-13-2002
kermi3

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.