Question 1129795
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<pre>
Let x be the amount (= the volume) of the 5% fruit juice (in gallons), and
let y be the amount (= the volume) of the 50% fruit juice.


Then you have two equations


     x +      y =     5     gallons   (1)    (the total volume)
0.05*x + 0.50*y = 0.4*5     gallons   (2)    (the volume of the pure juice).


The setup is completed.


To solve the system, I will apply the Substitution method.


For it, express x = 5-y from the first equation and substitute it into the second equation, replacing x. You will get


0.05*(5-y) + 0.5*y = 0.4*5       

0.25 - 0.05y + 0.5y = 2,

0.45y = 2 - 0.25

0.45y = 1.75  ====>  y = {{{1.75/0.45}}} = {{{((7/4))/((45/100))}}} = {{{((7/4))/((9/20))}}} = {{{(7*20)/(4*9)}}} = {{{(7*5)/9}}} = {{{35/9}}} = {{{3}}}{{{8/9}}}.


<U>Answer</U>.  {{{3}}}{{{8/9}}} of the 50% fruit juice and the rest  {{{5}}} - {{{3}}}{{{8/9}}} = {{{1}}}{{{1/9}}} gallons of the 5% fruit juice.


<U>Check</U>.  Equation (1):  {{{3}}}{{{8/9}}} + {{{1}}}{{{1/9}}} = 5.   ! Correct !


        Equation (2):  Left side of the eq. (2) is  {{{0.05*(10/9)}}} + {{{0.5*(35/9)}}} = {{{(1/100)*(50/9 + 1750/9)}}} = {{{(1/100)*(1800/9)}}} = 2 gallons of the pure juice.

                       Right side of the eq(2) is  0.4*5 = 2 gallons of the pure juice.


         Both sides are equal  <-------->  the solution (the answer) is 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.