Question 1092146
.
3 &nbsp;parts of the &nbsp;40% &nbsp;and &nbsp;1 part of the &nbsp;80%, &nbsp;i.e. &nbsp;9 liters of the &nbsp;40% &nbsp;and &nbsp;3 liters of the &nbsp;80%,  &nbsp;<U>IF TO SOLVE THE PROBLEM MENTALLY</U>


Let's check:  &nbsp;{{{(0.4*9 + 0.8*3)/12}}} = {{{(3.6 + 2.4)/12}}} = {{{6/12}}} = 0.5 = 50%.


Yes, &nbsp;it works.


Now I'll show you how to solve it using equation.


<pre>
Let x be the amount (the volume in liters) of the 40% solution.

Then the amount of the 80% solution is  (12-x) liters.


The "alcohol contents/concentration equation" is

{{{(0.4*x + 0.8*(12-x))/12}}} = 0.5.


Multiply by 12 both parts:

0.4x + 0.8*(12-x) = 6  ====>

0.4x + 9.6 - 0.8x = 6  ====>

9.6 - 6 = 0.8x - 0.4x  ====>  0.4x = 3.6 ===>  x = {{{3.6/0.4}}} = 9.


So, we get the same answer: 9 liters of the 40% solution and (12-9) = 3 liters of the 80% solution.
</pre>

Solved.



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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.


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.