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?
Last edited by Zewu; 11-13-2002 at 01:24 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.
-Govtcheez
[email protected]
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
Last edited by BMJ; 11-13-2002 at 01:50 PM.
I'd be delighted if you could explain for us how you got to this conclusion
Last edited by Zewu; 11-13-2002 at 02:04 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..
Last edited by tedde; 11-13-2002 at 02:18 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
.25d + .8c = .4*660
d + c = 660
Solve the system.
Edit: PJ beat me with a different way.
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?
"Owners of dogs will have noticed that, if you provide them with food and water and shelter and affection, they will think you are god. Whereas owners of cats are compelled to realize that, if you provide them with food and water and shelter and affection, they draw the conclusion that they are gods."
-Christopher Hitchens
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.
and the answer is: