Problem:
Jar contains four liters of a solution that is acid. Jar contains five liters of a solution that is acid. Jar contains one liter of a solution that is acid. From jar liters of the solution is added to jar , and the remainder of the solution in jar is added to jar . At the end both jar and jar contain solutions that are 50% acid. Given that and are relatively prime positive integers, find .
Solution:
If the contents of all three jars were mixed together, the mixture would be ten liters that is acid. Thus the total amount of acid in the three solutions is , so . When liters from jar are added to jar , the final proportion of acid in jar is . Solving gives , and so the requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions