SOLUTION: How many gallons of a 80% acid solution must be mixed with 50 gallons of a 16% solution to obtain a solution that is 70% acid?

Question 827351: How many gallons of a 80% acid solution must be mixed with 50 gallons of a 16% solution to obtain a solution that is 70% acid?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = gallons of 80%
y = gallons of 16%
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80x + 16y = 70(x + y)
y = 50
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put the system of linear equations into standard form:
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80x + 16y = 70x + 70y
y = 50
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10x - 54y = 0
y = 50
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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:
x = gallons of 80% = 270
y = gallons of 16% = 50
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system matrix
10 -54
0 1
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inverse of system matrix
0.1 5.4
0 1
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determinant of system matrix = 10
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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