Question 1106104
.
A car radiator needs a 70% antifreeze solution. The radiator now holds 20 liters of a 60% solution. 
How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
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<pre>
Let V be the volume to drain off from 20 liters of antifreeze.


<U>Step 1:  Draining</U>.  After draining,  you have 20-V liters of the 60% antifreeze.

                    It contains 0.60*(20-V) of pure antifreeze.


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

                     After the replacing,  you have the same total liquid volume of 20 liters.

                     It contains 0.60*(20-V) + V liters of pure antifreeze.



So, the antifreeze concentration after replacement is  {{{(0.60*(20-V)+V)/20}}}. 

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



Therefore, the concentration equation is 

{{{(0.60*(20-V)+V)/20}}} = 0.70.    (1)   


The setup is done and completed.


To solve the equation (1), multiply both sides by 20. You will get

0.6*(20-V) + V = 0.7*20,

12 - 0.6V + V = 14,

0.4V = 14 - 12 = 2  ====>  V = {{{2/0.4}}} = 5 liters.


<U>Answer</U>.  5 liters of the 60% antifreeze must be drained and replaced by 5 liters of pure antifreeze.


<U>Check</U>.   {{{(0.6*(20-5)+5)/20}}} = 0.7.   ! Correct !
</pre>


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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.