Question 1112665
<pre>
Let V be the volume to drain off from 26 quarts of antifreeze.


<U>Step 1:  Draining</U>.  After draining,  you have 26-V quarts of the 50% antifreeze.

                    It contains 0.50*(26-V) of pure antifreeze.


<U>Step 2:  Replacing</U>.  Then you add V quarts of the pure antifreeze (the replacing step).

                     After the replacing,  you have the same total liquid volume of 26 quarts.

                     It contains 0.50*(26-V) + V quarts of pure antifreeze.



So, the antifreeze concentration after replacement is  {{{(0.50*(26-V)+V)/26}}}. 

It is the ratio of the pure antifreeze volume to the total volume.



Therefore, your "concentration equation" is

{{{(0.50*(26-V)+V)/26}}} = 0.6.    (1)    


The setup is done and completed.


To solve the equation (1), multiply both sides by 26. You will get

0.50*(26-V) + V= 0.6*26,

13 - 0.5V + V= 15.6,

0.5V = 15.6 - 13 = 2.6  ====>  V = {{{2.6/0.5}}} = 5.2 liters.


<U>Answer</U>.  5.2 quarts of the 50% antifreeze must be drained and replaced by 5.2 quarts of pure antifreeze.


<U>Check</U>.   {{{(0.50*(26-5.2)+5.2)/26}}} = 0.6.    ! Correct !
</pre>


-----------------
There is entire bunch of introductory 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=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>

in this site.


Read them and become an expert in solution mixture word problems.
Notice that among these lessons there is one on antifreeze solutions marked by (*).



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 textbook in the section "<U>Word problems</U>" under the topic "<U>Mixture problems</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.