Question 1156558
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<pre>

Let x be the amount of the 20% alcohol solution (in gallons),
and y be the amount of the 50% alcohol solution.


Your first equation is

    x + y = 9                      (1)

for the total volume.


There are 0.2x gallons of the pure alcohol in the x gallons of the 20% solution,
and there are 0.5y gallons of the pure alcohol in the y gallons of the 50% solution.

So, there are, in total, 0.2x + 0.5y gallons of the pure alsohol in ingredients.


It should be equal to the amount of the the pure alcohol in the mixture,  0.3*9.

It gives you the second equation

    0.2x + 0.5y = 0.3*9    gallons   (2)


Thus you have the system of two equations, (1) and (2).


From equation (1), express  x = 9-y and substitute it into the second equation, replacing x You will get

    0.2*(9-y) + 0.5y = 2.7.


From this equation

    y = {{{(2.7 - 0.2*9)/(0.5-0.2)}}} = 3.


So, the problem is just solved.


<U>ANSWER</U>.  3 gallons of the 50% solution, and the rest, (9-3) = 6 gallons of the 20% solution.


<U>CHECK</U>.   I will calculate the concentration of the mixture. It is  {{{(0.5*3 + 0.2*6)/9}}} = 0.3 = 30%.   ! Precisely 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.