Question 1088264
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<pre>
Let x and y be the volumes (in liters, L) to be mixed.


Then one equation is "the volume" equation 

x + y = 60    (liters)     (1)

for the total volume.


The amount of "x" liters of the 2% solution contains 0.02x liters of pure alcohol.

The amount of "y" liters of the 6% solution contains 0.06y liters of pure alcohol.


Thus the mixture contains  0.02x + 0.06y liters of pure alcohol.

From the other side, the mixture contains 0.05*60 liters of pure alcohol.


It gives you the second equation, "pure alcohol contents equation"

0.02x + 0.06y = 0.05*60   (liters of pure alcohol)   (2)


Combining equations (1) and (2), you have this system of two linear equations for two unknowns

    x +     y = 60,     (3)
0.02x + 0.06y =  3.     (4)


Multiply equation (4) by 100 (both sides). You will get an equivalent system in the form

 x +  y =  60,          (5)
2x + 6y = 300           (6)

To solve it, express x = 60 - y from (5) and substitute into (6) replacing x. You will get

2(60-y) + 6y = 300,

120 - 2y + 6y = 300,

4y = 300 - 120   ====>  4y = 180  ====>  y = {{{180/4}}} = 45.


<U>Answer</U>.  45 liters of the 6% alcohol solution must be mixed with 60-45 = 15 liters of the 2% alcohol solution.
</pre>

Solved.



There is entire bunch of lessons covering various types of mixture problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson>Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson>More Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson>Solving typical word problems on mixtures for solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-antifreeze-solutions.lesson>Word problems on mixtures for antifreeze solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-word-problems-on-mixtures-for-dry-substances-coffee-nuts.lesson>Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-dry-substances-like-cookies-candies.lesson>Word problems on mixtures for dry substances like candies, dried fruits</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-dry-substances-like-soil-and-sand.lesson>Word problems on mixtures for dry substances like soil and sand</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-alloys.lesson>Word problems on mixtures for alloys</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problem-for-three-alloys.lesson>Advanced mixture problem for three alloys</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/OVERVIEW-of-lesson-on-word-problems-for-mixtures.lesson>OVERVIEW of lessons on word problems for mixtures</A>

in this site.


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


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Mixture problems</U".