Question 1126501
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            Since both @addingup and @josgarithmetic gave incorrect solutions and wrong answers, I came to fix everything.



<pre>
Let x be the volume of the pure acid to be added, in Liters.


Then the volume of the 10% acid should be 90-x.


Your equation is the balance of pure acid in both ingredients and in the mixture


    <U>pure acid</U> + <U>pure acid</U> = <U>total pure acid</U>,    or


    1x        + 0.1*(90-x) = 0.64*90.


Multiply by 100 both sides.


    100x + 900 - 10x = 64*90

    90x = 64*90 - 90

    x = 64 - 10


    x= 54    liters of the pure acid.


    and 36 liters of the 10% acid.


<U>Answer</U>.  54 liters of the pure acid  and  36 liters of the 10% acid.


<U>Check</U>.   {{{(54 + 0.1*36)/(54+36)}}} = 0.64 = 64% concentration.    ! Correct !
</pre>

Solved.


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It is a standard and typical mixture problem.


For introductory lessons covering various types of mixture word problems see

&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/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

in this site.


You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, &nbsp;from very detailed to very short.


Read them and become an expert in solution 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 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.