Question

At the canterbury dog fair, 1/4 of the poodles are also show dogs and 1/7 of the show dogs are poodles. What is the least possible number of dogs at the fair?

Answer 1

Answer:

10

Step-by-step explanation:

Let the number of show dogs = x

Let the number of poodles = y

So here,

1/7 dogs of x are poodles.

Also, 1/4 of y are show dogs

So,

1/7 of x = 1/4 of y

We can understand that Poodles are divisible by 4, because 1 out of 4 poodles is a show dog.

Similarly, show dogs are divisible by 7, because 1 show dog out of 7 are poodles.

/Least number divisible by 4 = 4

Least number divisible by 7 = 7/

So, the least number of poodles will be 4, out of which 1 is a show dog.

The least number of show dogs will be 7, out of which 1 is a poodle

So, poodles which are not show dogs = 3

Number of show dogs = 7 (including the 1 poodle)

Therefore, the least possible number of dogs = 3 + 7 = 10