A bag contains some red, some yellow and some blue beans.
The probability of picking a red bean at random is 0.2.
It is known that the ratio of yellow to blue beans is .
From the question we know
but we also know that ,
where is the number of red beans and is the total number of beans.
We also know that (2),
where is the number of yellow beads and is the number of blues.
From the ratio given ,
Substituting equations (1) and (3) into (2) we get .
Using (1), (4) and (5) to create a ratio,
So, the smallest number of beans is .