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### Solve for x in a Percentage Equation

```
Date: 2/5/96 at 17:56:20
From: Anonymous
Subject: word problem

Express as a function of x.

i) The volume of water that must be added to 5L of antifreeze to
make a solution that is x percent antifreeze.

ii) The volume of antifreeze that must be added to 5L of water to
make a solution that is x percent antifreeze

What are the domain and range of each function?

Graph the function.
```

```
Date: 6/18/96 at 13:31:1
From: Doctor Robert
Subject: Re: word problem

i) The percent antifreeze of a solution is the amount of
antifreeze divided by the total volume of the solution.
Let W be the volume of water added to 5 liters of
antifreeze(assumed to be 100 percent antifreeze).
Then the fraction of antifreeze is

x = 5/(5+W)

where the range is W>=0,and the domain is 0<x<1.

ii) x = A/(A+5) where A is the amount of pure antifreeze added
to 5 liters of water.  The domain of this function is
0 < = x < 1.  The range is A>= 0

-Doctor Robert,  The Math Forum

```
Associated Topics:
Middle School Fractions

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