Smallest square-valued bank of easy and medium items

A puzzle writer keeps a stock of easy and medium questions. Every easy one is valued at $3 and every medium one at $6. When one question is drawn uniformly at random from the stock, it is medium with probability $1/4$. The combined value of the entire stock, in dollars, is a perfect square. What is the least that total can be?

$225. The medium probability of $1/4$ forces three easy questions per medium one, so the stock splits into blocks worth $3\cdot3+6=15$ dollars. We need the least $n$ with $15n$ a perfect square, which is $n=15$, giving $225$.