Which jar is more contaminated?
You start with two jars – one contains only water, and the other an equal amount of oil. Your mischievous sibling grabs a one cup measure and scoops from the oil jar and pours it into the water jar. Hoping to reverse the process, you scoop one cup from the (now contaminated) water jar and pour it back into the oil jar. Now you realize both jars are contaminated. But is there more oil in the water jar, or water in the oil jar?
It might be tempting to do a lot of algebra to solve this problem. You might even question whether it can be solved – after all, do the oil and water mix, or do we scoop a different ratio out each time? But the answer is actually simpler. Any water missing from the water jar at the end must be in the oil jar. But because the jars start and end with the same total amount of liquid, all of that missing water must be replaced with the identical volume of oil. Similarly, any oil missing from the oil jar must be replaced with an identical volume of water. So there is exactly as much oil in the water jar as there is water in the oil jar. Don’t believe me? Take a look at the photo below – or better yet try it yourself!
Still don’t believe it? Replace oil and water with blue and red marbles. If we start and end with 20 marbles on the top and bottom, then any red marbles that went from the bottom to the top had to be replaced by the same number of blue marbles, and vice versa.
