2011 AIME I Problem 1

Jar A contains four liters of a solution that is 45\% acid. Jar B contains five liters of a solution that is 48\% acid. Jar C contains one liter of a solution that is k\% acid. From jar C, \frac{m}{n} liters of the solution is added to jar A, and the remainder of the solution in jar C is added to jar B. At the end both jar A and jar B contain solutions that are 50\% acid. Given that m and n are relatively prime positive integers, find k + 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.