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### Mixture Problem

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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
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/
```
Associated Topics:
High School Basic Algebra
High School Linear Equations
Middle School Algebra
Middle School Equations
Middle School Word Problems

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