Question

A pet store has only cats and dogs. the ratio of the number of cats to the number of dogs in the pet store is 2: 3. of the cats and ! of the dogs wear collars. if 48 animals wear collars, how many animals are in the pet store?

Answer 1

The total number of animals in the pet store is approximately 103.71.

Step-by-step explanation:

Let's assume that the number of cats in the pet store is 2x and the number of dogs is 3x, where x is a constant.

Since the ratio of cats to dogs is 2:3, we have the equation 2x/3x = 2/3.

Now, let's assume that the number of cats wearing collars is p and the number of dogs wearing collars is q. Given that p + q = 48, we can set up another equation.

We know that 2/3 of the cats wear collars, so p = 2/3 * 2x. Similarly, we know that 1/3 of the dogs wear collars, so q = 1/3 * 3x.

Substituting these values into the equation p + q = 48, we get (2/3 * 2x) + (1/3 * 3x) = 48.

Simplifying this equation gives us 4x/3 + x = 48.

Multiplying through by 3, we get 4x + 3x = 144.

Combining like terms, we have 7x = 144.

Finally, dividing both sides by 7 gives us x = 144/7.

Therefore, the total number of animals in the pet store is 2x + 3x = 5x = 5 * (144/7) = 103.71 (approx.).

Answer 2

The total number of animals in the pet store is 120.

Let the number of cats be 2x and the number of dogs be 3x (as the ratio is 2:3).

The total number of animals is 2x + 3x = 5x.

The fraction of animals wearing collars is (2/5) for cats and (1/3) for dogs.

Combining these, the total fraction of animals with collars is (2/5 + 1/3).

Multiplying this fraction by the total number of animals gives the number of animals with collars, which is 48.

Solving for x, we find x = 24.

Therefore, the total number of animals is 5x = 5 * 24 = 120.

So, there are 120 animals in the pet store, with the ratio of cats to dogs being 2:3. The calculation is based on the given information that 48 animals in the store wear collars, with 2/5 of cats and 1/3 of dogs having collars.