System of Equations and Gauss-JordanDate: 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/ |
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