SOLUTION: A chemist wants to make 700mL of a 6% acid solution by using 5% and 12% acid solutions. How much of each should she use?
Please do not use system of equations.
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Please do not use system of equations.
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Question 825463: A chemist wants to make 700mL of a 6% acid solution by using 5% and 12% acid solutions. How much of each should she use?
Please do not use system of equations. Found 2 solutions by TimothyLamb, josgarithmetic:Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! ---
5x + 12y = 6*700
x + y = 700
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put the system of linear equations into standard form
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5x + 12y = 4200
x + y = 700
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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answer by matrix method:
x = 600 mL of 5%
y = 100 mL of 12%
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system matrix
5 12
1 1
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inverse of system matrix
-0.14285714 1.7142857
0.14285714 -0.71428571
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determinant of system matrix = -7
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now solve by elimination:
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5x + 12y = 4200
(x + y = 700)*(-5)
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5x + 12y = 4200
-5x - 5y = -3500
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add the system:
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7y = 700
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y = 100
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x + y = 700
x = 700 - y
x = 700 - 100
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x = 600
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answer by elimination method:
x = 600 mL of 5%
y = 100 mL of 12%
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NOTE:
the answer by the matrix method agrees with the answer by the elimination method.
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