Date: 11/11/97 at 21:30:15 From: Erica Lower Subject: Mixture problems I am in ninth grade and in my first year of algebra. It was a breeze at first, but now it is getting very complicated. I know how to do the equation once it is set up, but the problem is that I can't figure out how to set them up. Example: Chris has 3 gallons of a solution that is 30 percent antifreeze, which he wants to use to winterize his car. How much pure antifreeze should he add to this solution so that the new solution will be 65 percent antifreeze? Thank you so much for your time. I appreciate it and I'm sure my class will too!
Date: 11/12/97 at 05:42:13 From: Doctor Mitteldorf Subject: Re: Mixture problems Dear Erica, Take heart! Everyone goes through a period of confusion about word problems. Translating words into useful equations is a skill that you can develop over a lifetime. The more you do, the better you'll get at it. Keep trying and don't be afraid to make mistakes. Follow the consequences of your reasoning, and try to learn from where it takes you. Go back and try something else. Whatever it takes. About antifreeze... Let's see, you start out with x gallons of antifreeze that's been mixed with y gallons of water, and the total is 3 gallons, so I'd say x + y = 3 is a good equation to start with. You also know that the solution is 30 percent antifreeze, so x/(x+y) = .30. Since you have two equations and two unknowns, these equations are enough to tell you both x and y. Maybe you should find x and y before going any further, and then you can write the next equation more simply. Now we want to add some more antifreeze until the total is 65 percent antifreeze. Say you're adding z gallons. The equation is (x+z)/(x+y+z) = 0.65 The x+z is the total amount of antifreeze, and the x+y+z is the total amount of solution, antifreeze+water. Since you already know x and y, you can put them into this equation and you'll just have a single equation with z in it. That should do the trick! One more thing. I think the person who made up this question was thinking more about algebra than about chemistry. Antifreeze and water really don't mix this way! Try it and see: take one measuring cup full of antifreeze and mix it with one measuring cup full of water. Let me know if the mixture you get is two cups or if it comes out more or less than two cups! -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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