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!!

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## About Nicole Bencze

I am an awesome newish math teacher who calls Delta School District her home.
I'm crazy in love with math and there's no place in this world I'd rather be than in a classroom showing my kidlets how amazing it can be!
Outside of teaching I'm quite the coffee addict and I live inside the fandom universe falling in love again and again with Lord of the Rings, Harry Potter, Mortal Instruments, Twilight, Hunger Games, Percy Jackson, Game of Thrones, Sherlock, Doctor Who, and a ton more.
My cat is my best friend and I'm way too invested in TV shows!
Thorough work from an inductive reasoning point of view – good that you tried lots of cases. One approach to try would be to make the dropper have x mL, and that may satisfy your desire for being convinced. Or… maybe not, especially after I tell you that all of your specific examples involve stirring the coke glass thoroughly – yet this is not needed! It’s quite mind-blowing actually! Hopefully we’ll have time to explore this quickly in class, and if not, feel free to explore a bit more on your own and I can provide some help if desired. (5/5)