2000 AIME I Problem 5

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?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.