# 2011 AIME I Problems/Problem 1

## 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 acid. From jar C, 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 and are relatively prime positive integers, find .

## Solution

There are L of acid in Jar A. There are L of acid in Jar B. And there are L of acid in Jar C. After transfering the solutions from jar C, there will be

L of solution in Jar A and L of acid in Jar A.

L of solution in Jar B and of acid in Jar B.
Since the solutions are 50% acid, we can multiply the amount of acid for each jar by 2, then equate them to the amount of solution.