SOLUTION: One hundred liters of a 50% solution of a chemical mixture is obtained by mixing a 60% solution with a 20% solution. Using a system of linear equations determine how many liters of

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Question 1091275: One hundred liters of a 50% solution of a chemical mixture is obtained by mixing a 60% solution with a 20% solution. Using a system of linear equations determine how many liters of each solution are required to obtain the 50% mixture. Solve the system using matrices.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x, volume of the 20% solution
y, volume of the 60% solution

Need: 50% solution concentration, 1 liter of it

Account for concentration and account for volume.


You can solve the system.




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(adjusted)
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Let x be the volume of the 20% solution,
    y be the volume of the 60% solution.


Your system of equations is

   x +     y = 100,        (1)     (account for the volume)
0.2x + 0.6*y = 0.5*100     (2)     (account for the pure solvent volume)


You can rewrite it equivalently in the form

   x +     y = 100,        (1')     (account for the volume)
0.2x + 0.6*y =  50.        (2')     (account for the pure solvent volume)


The system (1'),(2') is the standard form of equations for the mixture word problems.


You can solve it by applying any appropriate method.


There is a bunch of introductory lessons in this site covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive

Read them and become an expert in solution mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".



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