<PRE><B>Question 825251</B>
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This post contains three different questions.
I will answer the first question.
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question:
How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution?
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x = gallons of 20% solution
y = gallons of 50% solution
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20x + 50y = 30*9
x + y = 9
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put the system of linear equations into standard form
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20x + 50y = 270
x + y = 9
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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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solution by matrix method:
x = gallons of 20% solution = 6
y = gallons of 50% solution = 3
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system matrix
20 50
1 1
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inverse of system matrix
-0.033333333 1.6666667
0.033333333 -0.66666667
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determinant of system matrix = -30
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now the solution by elimination:
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20x + 50y = 270
(x + y = 9)*(-20)
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20x + 50y = 270
-20x - 20y = -180
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add the system:
30y = 90
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y = 3
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x + y = 9
x + 3 = 9
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x = 6
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solution by elimination method:
x = gallons of 20% solution = 6
y = gallons of 50% solution = 3
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NOTE:
solution by matrix method agrees with solution by elimination method
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Solve systems of linear equations up to 6-equations 6-variables:
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