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Applications of Linear Systems

Word problems using two equations and two unknowns

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Clean That Scrape, But Don't Get Burned!

Credit: Daniel Oines
Source: http://www.flickr.com/photos/dno1967b/8606348601/
License: CC BY-NC 3.0

Have you ever fallen off your bike and scraped your knee? Perhaps you cleaned that scrape with hydrogen peroxide. But did you know that not all hydrogen peroxide is created equally?

Why It Matters

In fact, high concentrations of hydrogen peroxide (30% or higher) are used as a component of rocket fuels and can burn the skin. What’s more, the Agency for Toxic Substances and Disease Registry warns that breathing in the vapors of even a 10% solution of hydrogen peroxide may result in severe lung irritation. You certainly don’t want to trade a scrape for something far worse!

The hydrogen peroxide that you find in your local drugstore, like the bottle above, is typically a 3% solution, whereas food-grade hydrogen peroxide usually comes in a 35% solution. The first is quite safe while the second is harmful, but chemists can combine the two to produce a hydrogen peroxide solution that falls anywhere in between—and they use linear systems to help them achieve the percent solution they’re aiming for.

See for yourself:

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Watch the following video to learn more about solving real-world systems of linear equations.


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  1. [1]^ Credit: Daniel Oines; Source: http://www.flickr.com/photos/dno1967b/8606348601/; License: CC BY-NC 3.0

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