Question 1103833
.
<pre>
Let x = the volume of the 15% acid (in liters) and 

let y = the volume of the 30% acid.


Then the volume of the 75% acid is 2y liters.


Then your equations are

    x +    y +       2y = 216,         (1)     (total volume)
0.15x + 0.3y + 0.75*(2y) = 0.25*216    (2)    (pure acid volume)


Simplify:

    x +   3y = 216,                    (3)
0.15x + 1.8y =  54.                    (4)


Simplify one more time by multiplying eq(4) by 100 (both sides)

    x +   3y =  216,                   (5)
  15x + 180y = 5400.                   (6)


Now multiply eq(5) by 15 (both sides). The modified system is

  15x +  45y = 3240,                   (7)
  15x + 180y = 5400.                   (8)


Next subtract eq(7) from eq(8).  The terms "15x" will cancel each other, 
and you will get a single equation for only one unknown "y".    (It is how the Elimination method works).

  180y - 45y = 5400 - 3240,

  135y = 2160  ====>  y = {{{2160/135}}} = 16.


<U>Answer</U>.  16 liters of the 30% solution,  16*2 = 32 of the 75% solution and the rest 216-(16+32) = 168 liters of the 15% solution.


<U>Check</U>.  0.3*16 + 0.75*32 + 0.15*168 = 54 liters of pure acid;

        0.25*216 = 54 liters of pure acid.   ! Correct !
</pre>

Solved.


-----------------
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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problems.lesson>Advanced mixture problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problem-for-three-alloys.lesson>Advanced mixture problem for three alloys</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.