SOLUTION: Solve the problem by using the Gauss-Jordan method to solve a system of equations. MIXING SOLUTIONS: A 5% solution of a drug is to be mixed with some 15% solution and some 10

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Solve the problem by using the Gauss-Jordan method to solve a system of equations. MIXING SOLUTIONS: A 5% solution of a drug is to be mixed with some 15% solution and some 10      Log On


   

Question 1089386: Solve the problem by using the Gauss-Jordan method to solve a system of equations.
MIXING SOLUTIONS:
A 5% solution of a drug is to be mixed with some 15% solution and some 10% solution to get 20 mL of 8% solution. The amount of 5% solution used must be 2 mL more than the sum of the other two solutions. How many milliliters of each solution should be used?
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
x, volume of the 5%
y, volume of the 10%
z, volume of the 15%

Converting the description into a system of equations:
system%285x%2B10y%2B15z=8%2A20%2Cx%2By%2Bz=20%2Cx=y%2Bz%2B2%29

Simplifying the system of equations:
system%28x%2B2y%2B3z=32%2Cx%2By%2Bz=20%2Cx-y-z=2%29

Matrix to begin:

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Finished solution:
system%28x=11%2Cy=6%2Cz=3%29