An animal shelter have 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
r:d = 2:5
find a common multiple for d
d:c = 15:35
r:d = 6:15
r:d:c = 6:15:35
1008/(6+15+35) = 18
so, there are
6*18 = 108 rabbits
15*18 = 270 dogs
35*18 = 630 cats
oh, ye. i got it. thanks for your help!
nice question
To find the number of rabbits in the shelter, we need to follow a step-by-step approach using the given information.
Step 1: Assign variables:
Let's assign variables to the unknown quantities.
Number of dogs = 3x
Number of cats = 7x
Number of rabbits = y
Step 2: Set up equations based on the ratios:
The ratio of dogs to cats is given as 3:7. Therefore, we can write the equation:
3x / 7x = 3/7
The ratio of rabbits to dogs is given as 2:5. Therefore, we can write the equation:
y / 3x = 2/5
Step 3: Solve the equations:
Let's start by solving the first equation:
3x / 7x = 3/7
Cross multiplying, we get:
3 * 7x = 3x * 7
21x = 21x
This equation is true for any nonzero value of x, therefore x can be any nonzero value.
Now, let's solve the second equation:
y / 3x = 2/5
Cross multiplying, we get:
5 * y = 3x * 2
5y = 6x
Dividing both sides by 6x, we get:
y = (6/5)x
Step 4: Finding the value of x:
Since x could be any nonzero value, we need more information to determine its exact value.
Step 5: Finding the number of rabbits:
Now that we have an equation for the number of rabbits in terms of x, we can't determine the exact number of rabbits without knowing the value of x. However, we do know that the number of rabbits must be a whole number since we can't have a fraction of a rabbit.
Without more information or any other restrictions, we are unable to determine the exact number of rabbits in the shelter.