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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-

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

Associated Topics:
High School Discrete Mathematics
High School Linear Algebra

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