MathDB
Jars of Acid Solution

Source:

March 18, 2011
rationumber theoryrelatively primeAMC

Problem Statement

Jar A contains four liters of a solution that is 45%45\% acid. Jar B contains five liters of a solution that is 48%48\% acid. Jar C contains one liter of a solution that is k%k\% acid. From jar C, mn\tfrac{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%50\% acid. Given that mm and nn are relatively prime positive integers, find k+m+nk+m+n.
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