Draining the Antifreeze

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

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

5. Let’s make our boxes

6. Let’s make our equation 10x + 100( 12 – x) = 300

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