Question 1147692
.
A tank containing liquid is filled with 40L of 70% salt solution. What volume of the solution to be taken 
and be filled up with 10L of water to make the concentration 50% salt solution?
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            The maximum possible concentration of salt in water is about  28%.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Then &nbsp;<U>saturation</U> &nbsp;occurs, &nbsp;and no more salt dissolves in water.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See this Wikipedia article https://en.wikipedia.org/wiki/Saline_water


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If to forget &nbsp;(to neglect) &nbsp;this saturation effect, &nbsp;then the problem can be solved in this way :



<pre>
Let W be the volume (in liters) of the 70% salt solution to take it off.


After taking off W liters of the 70% solution, you have (40-W) liters of the 70% solution, and you add 10 liters of water.


So, you have THIS "concentration" equation


    {{{(0.7*(40-W))/((40-W) + 10)}}} = 0.5.


It is your basic equation for the problem.
Simplify and solve for W. 


    0.7*(40-W) = 0.5*(50-W)

    0.7*40 - 0.7W = 0.5*50 - 0.5W

    0.7*40 - 0.5*50 = 0.7W - 0.5W

    28     - 25     = 0.2W

    3               = 0.2W

    W               = {{{3/0.2}}} = 15.


<U>ANSWER</U>.  15 liters of the 70% solution should be taken off and then 10 liters of water added.
</pre>

Solved.


--------------------


There is a bunch of introductory lessons in this site, &nbsp;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>


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


Your problem is very similar to relevant problems on antifreeze mixtures.
See the lesson marked (*) in the list above.


Also, &nbsp;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>".



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.