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

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.

Well, well, well, it seems like you've stumbled upon an interesting conundrum in your town! Let's have some fun unwrapping this little puzzle, shall we?

First, we know that 10% of the dogs think they are cats. So that means that out of the total number of dogs, 10% of them are impostor cats.

Next, we are given that 10% of the cats think they are dogs. So, similarly, 10% of the total number of cats are impostor dogs.

Now, you say that 20% of all the animals tested thought they were cats. So, let's do some quick math. If 20% of the animals tested thought they were cats, that means that 20% of the total number of dogs PLUS 20% of the total number of cats equals 20% of ALL animals in the town.

Here comes the punchline: Since we know 10% of the dogs are impostor cats and 10% of the cats are impostor dogs, we can conclude that the remaining 10% of the animals who think they are cats are the actual cats in the town!

To find out the percentage of all cats and dogs who are really cats, we need to add up the impostor cats (10% of dogs) and the actual cats (10% of all animals tested), which gives us a total of 20%.

So, the answer is C. 20%! The actual cats and the impostor cats make up 20% of all the animals in the town. Isn't that quite the menagerie of confused creatures?

Remember, folks, math can be a barrel of laughs if you approach it with a sense of humor. Keep those questions rolling in, and Clown Bot is here to bring the giggles while providing answers!

To solve this problem, let's break it down step by step:

Step 1: Let's assume there are a total of 100 cats and dogs in the town.

Step 2: From the given information, we know that 20% of them (or 20 cats and dogs) think they are cats.

Step 3: We also know that 10% of the dogs think they are cats. So, 10% of the dogs would be 10 dogs.

Step 4: Therefore, out of the 20 cats and dogs who think they are cats, 10 of them are actually dogs.

Step 5: Now, we can subtract the dogs who think they are cats from the total number of cats and dogs who think they are cats: 20 - 10 = 10.

Step 6: Finally, we can calculate the percentage of all cats and dogs who are actually cats: (10 / 100) * 100 = 10%.

So, the correct answer is 10%. Therefore, the correct option is:

A. 12.5

To solve this problem, we need to analyze the information given and break it down step by step.

First, let's assume that there are 100 cats and dogs in total in the town. Since we're given that 20% of them think they are cats, that means 20 out of 100 cats and dogs think they are cats.

Next, we are told that 10% of the dogs think they are cats. Since we know that 20 out of 100 animals think they are cats, and 10% of them are dogs, that means 10% of the 20 animals that think they are cats are actually dogs.

Therefore, 10% of 20, which is 2, are dogs that think they are cats. So, out of the original 20 animals that think they are cats, 2 are actually dogs.

Now, subtracting the 2 dogs from the original 20 animals, we are left with 18 animals that are truly cats.

Since we assumed there were 100 cats and dogs in total, and we found that 18 of them are cats, we can conclude that the percentage of animals that are truly cats is 18%.

Therefore, the correct answer to the question is B. 18%.