A certain 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. 1/4 of the cats and 1/2 of the dogs wear collars. If there are 48 animals that wear collars, how many animals are in the pet store?
120 Animals
Let's assume that the number of cats in the pet store is 2x and the number of dogs is 3x.
According to the given information, 1/4 of the cats wear collars, which means (1/4) * 2x = x/2 cats wear collars.
Similarly, 1/2 of the dogs wear collars, which means (1/2) * 3x = (3/2)x dogs wear collars.
The total number of animals wearing collars is the sum of cats and dogs wearing collars: x/2 + (3/2)x = 48.
To simplify the equation, we can multiply all the terms by 2 to get rid of the fraction: 2(x/2) + 2(3/2)x = 2(48).
This simplifies to: x + 3x = 96.
Combining like terms, we get: 4x = 96.
Dividing both sides by 4, we find: x = 24.
Now that we know x, we can find the number of cats and dogs in the pet store.
The number of cats is 2x = 2 * 24 = 48.
The number of dogs is 3x = 3 * 24 = 72.
The total number of animals in the pet store is the sum of cats and dogs: 48 + 72 = 120.
Therefore, there are 120 animals in the pet store.
To solve this problem, we need to first determine the number of animals in the pet store. Let's suppose the number of cats is represented by 2x, and the number of dogs is represented by 3x, where x is a positive integer.
Now, we can find the number of cats wearing collars and the number of dogs wearing collars.
Since 1/4 of the cats wear collars, the number of cats wearing collars is (1/4)(2x) = x/2.
Likewise, since 1/2 of the dogs wear collars, the number of dogs wearing collars is (1/2)(3x) = (3/2)x.
According to the given information, the total number of animals that wear collars is 48.
Therefore, the equation is:
(x/2) + (3/2)x = 48
To solve this equation, we can begin by multiplying both sides of the equation by 2 to eliminate the fraction:
2(x/2) + 2(3/2)x = 48(2)
x + 3x = 96
4x = 96
x = 96/4
x = 24
Now that we have found the value of x, we can substitute it back into our earlier expressions to find the number of cats and dogs in the pet store.
The number of cats = 2x = 2(24) = 48 cats.
The number of dogs = 3x = 3(24) = 72 dogs.
To find the total number of animals in the pet store, we add the number of cats and dogs:
Total number of animals = 48 (cats) + 72 (dogs) = 120 animals.
Therefore, there are 120 animals in the pet store.