Answer: The pet store has a total of 48 cats + 72 dogs = 120 animals in total.
Explanation:
To find the number of animals in the pet store, we need to determine the number of cats and dogs separately.
Given that the ratio of cats to dogs is 2:3, let's assume the number of cats is 2x and the number of dogs is 3x.
Now, we know that 1/4 of the cats wear collars, so the number of cats wearing collars is 1/4 * 2x = x/2.
Similarly, 1/2 of the dogs wear collars, so the number of dogs wearing collars is 1/2 * 3x = 3x/2.
According to the problem, 48 animals wear collars. So, we can set up the following equation: x/2 + 3x/2 = 48.
To solve this equation, we need to get rid of the fractions. We can do this by multiplying the entire equation by 2:
2 * (x/2) + 2 * (3x/2) = 2 * 48.
This simplifies to x + 3x = 96.
Combining like terms, we have 4x = 96.
Dividing both sides by 4, we get x = 24.
Now that we know x, we can find the number of cats and dogs. The number of cats is 2x, so it is 2 * 24 = 48.
The number of dogs is 3x, so it is 3 * 24 = 72.
I hope this help.