Each of two boxes contains both black and white marbles, and the total number of marbles in the two boxes is $$25.$$ One marble is taken out of each box randomly. The probability that both marbles are black is $$\frac{27}{50},$$ and the probability that both marbles are white is $$\frac{m}{n},$$ where $$m$$ and $$n$$ are relatively prime positive integers. What is $$m + n$$?

(第十八届AIME1 2000 第5题)