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 total number of poodles = $x$

Let the total number of show dogs = $y$

$\frac{1}{4}$ of the poodles are show dogs

and

$\frac{1}{7}$  of the show dogs are poodles

$\therefore \dfrac{1}{4}x = \dfrac{1}{7} y$

As per the question statement, $x$ must be divisible by 4 and

$y$ must be divisible by 7.

And we have to find the least number of dogs.

So, least number divisible by 4 = 4 and

Least number divisible by 7 = 7

So, least values of $x$ i.e. poodles = 4 in which we have 1 show dog

Hence, 3 are not show dogs.

and least value of show dogs i.e. $y$ = 7 (it includes the one poodle which is also show dog).

So, least number of dogs at the fair = 7 + 3 = 10