Sitting on your kitchen table are two cups one contains oran

Sitting on your kitchen table are two cups, one contains orange juice and the other contains the exact same amount of apple juice. Your roommate comes in and takes some amount of orange juice from the cup, adds it to the apple juice cup and mixes it well. She then takes the exact same amount from the mixture, returns it to the orange juice cup and mixes well. After your roomate is done does the original apple juice cup have a higher percentage of orange jucie or the orange juice cup a higher percentage of apple juice? Justify your answer mathematically with a specific case and a general case.

Solution

If I