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.

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
---
put the system of linear equations into standard form
---
5x + 12y = 4200
x + y = 700
---
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
---
answer by matrix method:
x = 600 mL of 5%
y = 100 mL of 12%
---
system matrix
5 12
1 1
---
inverse of system matrix
-0.14285714 1.7142857
0.14285714 -0.71428571
---
determinant of system matrix = -7
---
now solve by elimination:
---
5x + 12y = 4200
(x + y = 700)*(-5)
---
5x + 12y = 4200
-5x - 5y = -3500
---
add the system:
---
7y = 700
---
y = 100
---
x + y = 700
x = 700 - y
x = 700 - 100
---
x = 600
---
answer by elimination method:
x = 600 mL of 5%
y = 100 mL of 12%
---
NOTE:
the answer by the matrix method agrees with the answer by the elimination method.
---
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 4-equations 4-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Look for the Mixture lesson linked in my profile for "...two concentrations for known amount of mixture".
RELATED QUESTIONS
A chemist wants to make 700mL of a 6% acid solution by using 5% and 12% acid solutions.... (answered by josmiceli)
A chemist wants to make 700 mL of a 6% nitric acid solution by using 5% and 12% nitric... (answered by TimothyLamb)
A chemist mixes an 11% acid solution with a 4 % acid solution . How many milliters of... (answered by lwsshak3)
A chemist wants to make 60 ml of a 17% acid solution by mixing a 12% acid solution and an (answered by ewatrrr)
A chemist wants to make 200ml of an acid solution with a concentration of 48%. He wants... (answered by josgarithmetic)
A chemist is mixing a solution that is 2% acid and another solution that is 8% acid. She... (answered by josgarithmetic)
a chemist is mixing a solution that is 2% acid and another solution that is 8% acid. She... (answered by Alan3354,josgarithmetic)
A chemist wants to make 54 mL of a 17% acid solution by mixing a 13% acid solution and an (answered by checkley77)
A chemist has three different acid solutions. The first acid solution contains 15% acid,... (answered by ikleyn,josgarithmetic)