In my town some of the animals are really strange. Ten percent of the dogs think that they are cats and ten percent of the cats think they are dogs. All the other cats and dogs are perfectly normal. One day I tested all the cats and dogs in the town and found that 20% of them thought that they were cats. What percentage of all cats and dogs really were cats?

Question

In my town some of the animals are really strange. Ten percent of the dogs think that they are cats and ten percent of the cats think they are dogs. All the other cats and dogs are perfectly normal. One day I tested all the cats and dogs in the town and found that 20% of them thought that they were cats. What percentage of all cats and dogs really were cats?
A. 12.5
B. 18
C. 20
D. 22

can someone please help been stuck on this for a while

MathMate · Answer

In summary,
90% of cats and 10% of dogs think they were cats.

So if the population is made up of C cats and D dogs, then
(0.9C+0.1D)/(C+D)=0.2

Let x=C/(C+D), then D/(C+D)=1-x
0.9x+0.1(1-x)=0.2
isolate x and solve
0.9x-0.1x=0.2-0.1
0.8x=0.1
x=0.125

=> 12.5% of the population are cats.