An animal shelter has 1008 cats, dogs and rabbits. The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number of rabbits to the number of dogs is 2:5. How many rabbits are there in the shelter?

d/c = 3/7 so c = 7d/3

r/d = 2/5 so d = 5r/2

r+d+c = 1008
r + 5r/2 + 7(5r/2)/3 = 1008
multiply by 6 to clear fractions
6r + 15r + 35r = 6048
56r = 6048
r = 108

still confused

To find the number of rabbits in the shelter, we need to follow a few steps:

Step 1: Find the number of dogs and cats in the shelter.
Given that the ratio of dogs to cats is 3:7, we can set up an equation:
3x + 7x = 1008
10x = 1008
x = 100.8
Since the number of animals must be a whole number, we can notice that 10x should be divisible by 10. Therefore, let's round down x to 100.

So the number of dogs = 3x = 3 * 100 = 300
And the number of cats = 7x = 7 * 100 = 700

Step 2: Find the number of rabbits.
Given that the ratio of rabbits to dogs is 2:5, we can set up another equation:
2y + 5y = 1008
7y = 1008
y = 144
So the number of rabbits = 2y = 2 * 144 = 288

Therefore, there are 288 rabbits in the shelter.