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Draining the Antifreeze

Your car holds 12 liters of a 10% antifreeze solution and needs to be prepared for winter with a 25% mixture. This problem can be confusing! To achieve this, you must drain a portion of the existing solution and replace it with pure antifreeze. By solving the equation derived from the mixture, we find that draining 10 liters of the current solution and replacing it with pure antifreeze gives us the desired concentration. This approach clarifies the steps needed to ensure your vehicle is winter-ready without the mental confusion.

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Draining the Antifreeze

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  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

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