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← Mixture Problem - Visualizing Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. Now that we've done some interest problems, let's try a mixture one. Mixture
  2. problems like this are helpful if you're at home and you want to make lemonade
  3. or punch. Usually, you're trying to make a different concentration than what you
  4. already have in your fridge. Scientists also use this approach when they're
  5. trying to make different concentrations of chemical solutions in the laboratory.
  6. Let's see how it works. Let's use the same approach as before with rates and
  7. amounts to try and set up equations. The wording is slightly different here
  8. because we're working with volumes and percentages, but I think you'll see a
  9. pattern. For this problem we have 5 gallons of a punch mix with 65% water. We
  10. want to mix it with a punch mix that's 80% water. So that way we get a mix
  11. that's 75% water in the end. The question is, how much of this 80% mixture
  12. should we use? These are the two equations that we're going to try and set up.
  13. The first one takes into the account the gallons of water. For example, the
  14. first volume that I have is 5 gallons of punch mix. This punch mix is 65% water.
  15. So if I take my percentage of water and multiply it by the gallons of punch,
  16. I'll get my gallons of water. I change 65% to its decimal, and multiply by 5, to
  17. get 3.25 or 3 and 25 hundredths. Remember the question can help us identify the
  18. variable. We don't know how much punch mix we need that's 80%, so I'm going to
  19. let that variable be x. Using x, and the information in the problem, I want you
  20. to complete our equation. What should go in these boxes? Mixes. Don't worry
  21. about volume 3. We actually don't know that quantity yet.