Answer:
10
Step-by-step explanation:
Let the total number of poodles = [tex]x[/tex]
Let the total number of show dogs = [tex]y[/tex]
[tex]\frac{1}{4}[/tex] of the poodles are show dogs
and
[tex]\frac{1}{7}[/tex] of the show dogs are poodles
[tex]\therefore \dfrac{1}{4}x = \dfrac{1}{7} y[/tex]
As per the question statement, [tex]x[/tex] must be divisible by 4 and
[tex]y[/tex] 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 [tex]x[/tex] 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. [tex]y[/tex] = 7 (it includes the one poodle which is also show dog).
So, least number of dogs at the fair = 7 + 3 = 10
