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 \mathrm{C}, \frac{m}{n} liters of the solution is added to jar \mathrm{A}, and the remainder of the solution in jar \mathrm{C} is added to jar \mathrm{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.