In a pet store there are 4 more cats than dogs and the ratio of cats to dogs is 12 to 9.What is the total number of cats and dogs in the pet store?
let the number of cats be 12x
let the number of dogs be 9x
12x - 9x = 4
3x=4
x = 4/3
number of cats = 12x = 12(4/3) = 16
number of dogs = 9(4/3) = 12
for a total of 28 cats and dogs.
check:
16:12 = 4:3 or the given 12:9
cats - dogs = 16-12 = 4 , thus 4 more cats than dogs
To find the total number of cats and dogs in the pet store, we need to determine the number of cats and dogs individually.
Let's start with the ratio given: 12 cats to 9 dogs. We can simplify this ratio by dividing both numbers by the greatest common divisor (GCD) of 12 and 9, which is 3. Simplifying the ratio, we get 4 cats to 3 dogs.
Given that there are 4 more cats than dogs, we can set up the equation: Cat Count = Dog Count + 4.
Substituting the simplified ratio, we can write: 4 = 3 + 4.
By solving this equation, we find that the number of dogs is 3.
To find the number of cats, we can substitute the value of dogs (3) back into the equation: Cat Count = 3 + 4, which equals 7.
So the total number of cats and dogs in the pet store is 7 + 3 = 10.