Question 1094062
.
How many gallons of a fruit drink that is 50% real juice must be mixed with a fruit drink that is 20% real juice 
to obtain 12 gallons of a fruit drink that is 40% real juice?
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<pre>
Let "x" be the volume (in gallons) of the 50% real juice, which is under the question.


Then the volume of the 20% of the fruit juice to mix is 12-x gallons.


The volume of the pure juice in x gallons of 50% real juice is 0.5x gallons.

The volume of the pure juice in (12-x) gallons of 20% real juice is 0.2*(12-x)) gallons.

The total volume of the pure juice in the mix is the sum of these amounts, i.e.

 0.5x  + 0.2*(12-x) gallons.

The concentration of pure juice in the mixture is  this fraction {{{(0.5x  + 0.2*(12-x))/12}}}.

According to the condition, it must be equal to 40%, or 0.4.


It gives you an equation 

{{{(0.5x  + 0.2*(12-x))/12}}} = 0.4.


It is your governing equation to find x.

To solve it, multiply both sides by 12. You will get

0.5x + 0.2*(12-x) = 0.4*12,

0.5x + 2.4 - 0.2x = 4.8,

0.5x - 0.2x = 4.8 - 2.4,

0.3x = 2.4  ====>  x = {{{2.4/0.3}}} = {{{24/3}}} = 8.


<U>Answer</U>.  You need to use 8 gallons of 50% real juice and (12-8) = 4 gallons of 20% real juice.

<U>Check</U>.   8*0.5 + 4*0.2 = 4.8.   12*0.4 = 4.8.   ! Correct !
</pre>

Solved.



I prefer do not use the tables at all when solving such problems.
Simple logic leads you step by step along the solution from the beginning to the end, if you do know and understand this logic.


Making table only distract you from the solution.


But I do not insist that my way is the only applicable.


I think that the tables play the role of crutches.


If you do understand the logic, you do not need tables.


And working to understand the logic is your goal.


The way to it is practice.



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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.



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By the way, writing by @gosgarithmetic is <U>I N C O R R E C T</U>.