Question

The ratio of cats to dogs in a room is 2:3. Five more cats enter the room, and then the ratio of cats to dogs is 9:11.How many cats and dogs were in the room to begin with?

Answer 1

So,

If the ratio of cats to dogs in the room is 2:3, that means that there are 2 cats per each 3 dogs.

Notice the following sequence:

Initial:

Cats: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Dogs: 3 6 9 12 15 18 21 24 27 30 33

After 5 more cats, the ratio is:

Cats: 0 9 18 27 36

Dogs: 0 11 22 33 44

We look for the situation where the number of dogs is the same and there are 5 more cats.

Therefore, there were 22 cats and 33 dogs at the beginning.