SOLUTION: I want to make 2 gallons of a drink that is 60% cranberry juice and 40% apple juice. How many gallons of 100% apple juice do I need to mix with an 80% cranberry/20% apple blend to

Question 826380: I want to make 2 gallons of a drink that is 60% cranberry juice and 40% apple juice. How many gallons of 100% apple juice do I need to mix with an 80% cranberry/20% apple blend to achieve this result?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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volumes:
x = 100% apple juice
y = 80/20 cranberry/apple juice
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cranberry:
60*2 = 0x + 80y
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apple:
40*2 = 100x + 20y
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linear system:
---
120 = 80y
80 = 100x + 20y
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put the system of linear equations into standard form:
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80y = 120
100x + 20y = 80
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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
---
solution:
x = 100% apple juice = 0.5 gallons
y = 80/20 cranberry/apple juice = 1.5 gallons
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system matrix
0 80
100 20
---
inverse of system matrix
-0.0025 0.01
0.0125 0
---
determinant of system matrix = -8000
---
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
---
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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