System of Equations and Gauss-Jordan

Date: 11/29/98 at 07:10:47
From: Nia Jones
Subject: Systems of equations - Using the Gauss-Jordan method

I'm having trouble setting up this kind of problem:

A 5% solution of a drug is to be mixed with some 15% solution and 
some 10% solution to get 20 ml of an 8% solution.

Thanks,
Nia

Date: 11/29/98 at 07:53:47
From: Doctor Jerry
Subject: Re: Systems of equations - Using the Gauss-Jordan method

Hi Nia,

There isn't enough information here for just one solution.

If x, y, and z are the amounts of the 5%, 15%, and 10% solutions needed 
to get 20 ml of 8%, then:

   x + y + z = 20  (solution equation)

and

   0.05x + 0.15y + 0.10z = 0.08*20  (drug equation).

Applying the Gauss-Jordan method:


   1   1   1     20
   5  15  10    160
 
   1   1   1     20
   0  10   5     60

   1   0   1/2   14
   0   1   1/2    6

So:

   x = 14 - z/2
   y = 6 - z/2 

Choose z as any non-negative number and so that x and y remain non-
negative. These are your constraints. 

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/