Question 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 $k + m + n.$