1. Draining the Antifreeze A Very Confusing Mixture Problem

2. The Problem Your car can hold 12 liters of anti-freeze. It currently has a 10% antifreeze solution. Winter is on the way! How much antifreeze do you need to drain and replace with pure antifreeze to make it a 25% solution?

3. The Confusion 1.Drain? We have only done problems where we add things together. Drain? What am I supposed to do with drain? 2.Pure antifreeze? Why did they say pure antifreeze?

4. The Confusion 1.Drain? 1.We are mentally going to drain all the antifreeze and put it in a pail. 2.Then we’re going to add antifreeze from the pail and some pure antifreeze. 3.Voila! - a familiar mixture problem. 2.Pure anti-freeze? The percentage of antifreeze in pure anti-freeze is 100%.

5. Let’s make our boxes # liters % Liters antifreeze old mixx1010x Pure12 - x100100( 12 – x) New mix1225300

6. Let’s make our equation 10x + 100( 12 – x) = 300 Liters antifreeze Antifreeze in old mix10x Antifreeze in pure100( 12 – x) Antifreeze in new mix300

7. Now let’s solve 10x + 100( 12 – x) = 300 10x + 1200 - 100x = 300 - 90x = 300 – 1200 - 90x = - 900 x = 10

8. Now let’s check We’ve kept 10 liters of our old 10% solution. That’s 1 liter of antifreeze. We have 2 liters of the pure stuff. That’s 2 liters of antifreeze. 1 + 2 = 3 liters of antifreeze. We wanted 25% of the 12 liters to be antifreeze. 25% of 12 =.25 ( 12 ) = 3 Hooray!

9. Don’t Allow Brain Drain! Drain? Drain it all into a pail and mix it back in like a regular problem. Pure Antifreeze? 100% antifreeze