Question 1165827
.
A flask contains 500 ml of an 80% alcohol solution in water. How much of this solution must be drawn off and replaced by water 
to obtain a solution having a concentration of 25% alcohol?
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<pre>
Let V be the volume to drain off from 500 mL of the original mixture.


<U>Step 1:  Draining</U>.  After draining,  you have 500-V mL of the 80% mixture.


<U>Step 2:  Replacing</U>.  Then you add V mL of water (the replacing step).

                     After the replacing,  you have the same total liquid volume of 500 mL.


It contains  0.8*(500-V)  of the pure alcohol.


So, your "concentration equation" is


    {{{(0.8*(500-V))/500}}} = 0.25.    (1)


The setup is done and completed.


Now you need to solve your basic equation  (1).  Multiply both sides by 500.


    0.8*(500-V) = 0.25*500

    0.8*500 - 0.8V = 125

    400     - 125  = 0.8V

    V = {{{275/0.8}}} = 343.75 mL.


<U>Answer</U>.  343.75 mL of the original mixture should be drained and replaced with water.
</pre>

Solved.


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It is a standard and typical mixture problem.


In this site, there is a bunch of lessons, &nbsp;covering various types of mixture problems. &nbsp;See introductory lessons

&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>


Of these lessons, the closest solutions to your problem you will find in the lesson marked (*) in the list.


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



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.