Link: Coke and Sprite Problem
This was an interesting problem to work on. I only watched the video twice, and both times I spent pausing and staring to see how much liquid was being transferred in that eye dropper. Right away, I knew that would be my key to solving this problem. Every time I watched the video though, I failed at figuring it out. How frustrating! I knew exactly how I wanted to solve this problem, and yet I had a key numerical value missing and therefore couldn’t really go anywhere. So I started googling how much the average eye dropper would hold.. I finally agreed upon the fact that they hold anywhere between 5 and 15ml so I knew I had a few calculations ahead of me. Now I had everything I needed to know to solve the problem! Being the avid pop drinker that I am I knew that each can contained 355ml. My method was simple: assuming the eyedropper held x ml of pop, I would do a step by step percentage calculation of the original pop and the new one, based on the new total quantity of pop and how much of each were mixed in. My instincts told me that it would probably end up being the same (assuming we transferred the same amount both times) but another part of me was dead set on the fact that that was way too obvious of a solution and that couldn’t be true. Another part of me was tempted to try it out and taste them to confirm my results, haha. In the end I did the calculations a ton of times with the eyedropper holding 5 ml, 10 ml, 11 ml, 12 ml, 13 ml, 14 ml, and finally 15 ml. They all gave me the same answer: the percentage of original pop was identical in both of them. I redid all the calculations with more decimal points because I just didn’t want to believe that they had equal concentrations! In fact I still don’t want to believe that they have different concentrations, but I have no clue how to prove that! So while the math is right in front of me, I still find myself pondering other ways to do this problem in hopes of getting a different answer, but I still can’t think of anything! Frustrating!!