The ratio of the number of cats to the number of birds at the shp is 2 : 5. The ratio of the number of birds to the number of birds to the number of rabbits is 1:3. What is the ratio of the number of cats to the number of birds to the number of rabbits. If there are 30 rabbits, how many cats are there at the pet shop?
To solve this problem, we can break it down into two steps:
Step 1: Find the ratio of cats to birds to rabbits.
Step 2: Determine the number of cats based on the given ratio and the known number of rabbits.
Step 1: Find the ratio of cats to birds to rabbits.
The ratio of cats to birds is given as 2:5, and the ratio of birds to rabbits is given as 1:3. We can calculate the overall ratio by multiplying these two ratios together.
Ratio of cats to birds to rabbits = (cats to birds) × (birds to rabbits)
= (2:5) × (1:3)
= (2/5) × (1/3)
= 2/15
So, the ratio of cats to birds to rabbits is 2:5:15.
Step 2: Determine the number of cats based on the given ratio and number of rabbits.
Since we know the ratio of cats to birds to rabbits is 2:5:15, and the information given is that there are 30 rabbits, we can set up a proportion to find the number of cats.
cats : birds : rabbits = 2 : 5 : 15
We know the number of rabbits is 30, so we can substitute that value into the proportion:
2/5 = cats/30
To solve for cats, we cross-multiply and solve for the unknown:
2 × 30 = 5 × cats
60 = 5 × cats
cats = 60/5
cats = 12
Therefore, there are 12 cats at the pet shop.
c:b = 2:5
b:r = 1:3 = 5:15
So,
c:b:r = 2:5:15
So, if r=30,
c:30 = 2:15
c = 4