Question 1155447
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<pre>

Let x be the volume of the 80% mixture to mix (in mL),

Then the volume of the 50% mixture is (270-x) mL.


The total volume of the pure alcohol in ingredients is  0.8*x + 0.50*(270-x)  mL,

and it should be equal to the volume of the pure alcohol in the mixture, which is  0.55*270.


So, your equation is

    0.8*x + 0.50*(270-x) = 0.55*270   milliliters of the pure alcohol.


From the equation

    x = {{{(0.55*270 - 0.50*270)/(0.8-0.50)}}} = 45.


<U>ANSWER</U>.  45 ml of the 80% mixture and the rest  270-45 = 225 ml of the 50% mixture.


<U>CHECK</U>.  I will check for the concentration  {{{(0.8*45 + 0.50*225)/270}}} = 0.55 = 55%.     ! Precisely correct !
</pre>

Solved.


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


Read them 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.