Question 1118742
.<pre>
Let x be the volume (in pints) of the 40% fruit juice to mix.


Then the volume of the 100% juice to add is (18-x) pints.


The volume of the pure juice in the mixture thus is 0.4x + (18-x) pints.


The total volume is 18 pints.


Hence, the concentration of the mixture = {{{Pure_Juice_Volume/Total_Volume}}} = {{{(0.4x + (18-x))/18}}}.


According to the condition, it must be 55%, or 0.55.  It gives you an equation


{{{(0.4x + (18-x))/18}}} = 0.55.     (1)


To solve it, multiply both sides by 14 and then simplify it step by step:


0.4x + 18 - x = 18*0.55

-0.6x = 18*0.55 - 18 = -8.1

x = {{{(-8.1)/(-0.6)}}} = 13.5 pints.


<U>Check</U>.  You need to check if the equation (1) is valid.


        {{{(0.4*13.5 + (18-13.5))/18}}} = 0.55.     ! Correct !


<U>Answer</U>.  13.5 pints of the 40% juice should be mixed with (18-13.5) = 4.5 pints of the pure juice.
</pre>

Solved.


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For introductory lessons covering various types of mixture 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/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 the 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 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.