By: Nick Spencer, Sam Marcoe, Elizabeth Englehart, Grayson Windle

This activity is based off of Dan Meyer’s “Coke vs. Sprite” activity.  In this activity, Dan has a glass of coke, and a glass of sprite, containing equal amounts.  Dan uses a dropper to take some of the sprite and drop it into the coke, creating a coke/sprite mixture.  He then uses the dropper to take some of the coke/sprite mixture, and drops it back into the original sprite.

Dan then asks us this: Which glass contains more of its original soda?

Step 1: Our group began our investigation with a visual representation via drawings in order to solve this problem.  In the figure below, the top two circles represent our original glasses of coke and sprite, each containing 100mL of themselves.

Step 2: Next, we have the dropper extract 10mL of the sprite, and drop it into the coke.  Now we are left with a glass containing 100mL of coke and 10mL of sprite, and a glass containing 90mL of sprite.

Step 3: For the next step, our dropper takes 10mL of the coke/sprite mixture, which we will say contains 9.1mL of coke and 0.9mL of sprite, and drops this into the original sprite glass.

Step 4: Here we do some math.  After adding the coke/sprite mixture into the sprite glass, we find that the original coke glass now has 90.9mL of coke with 9.1mL of sprite, and our sprite glass has 90.9mL of sprite with 9.1mL of coke.

Conclusion: So, which glass contained more of the original soda?
Coke Glass: 90.9mL Coke & 9.1mL Sprite
Sprite Glass: 90.9mL Sprite & 9.1mL Coke

We find that the glasses actually end up containing equal amounts of their original sodas.  We also discovered that this outcome would be the same regardless of the amount of extraction from the glasses.  Had we began with taking say 20mL from the Sprite (leaving 80mL) and putting it into the Coke (which now has 100mL of Coke and 20mL of Sprite), and then taken 20mL of the Coke/Sprite mixture (lets say the dropper has 15mL of Coke and 5mL of Sprite) and then dropped this into the Sprite glass, we would simply find that each glass now contains 85mL of the original soda, and 15mL from the other soda.

CCSS: CCSS.MATH.CONTENT.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.