Question 1138413
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<pre>

In this problem, concentrations are the ratios of a salt mass (in grams) to the volume of a mixture (in milliliters).



Let x be the amount of the 5%  solution needed (in milliliters), and

let y be the amount of the 11%  solution needed.



The mass of the salt in the 5% mixture  is 0.05x grams.

The mass of the salt in the 11% mixture is 0.11y grams.

The resulting mixture contains  0.05x + 0.11y grams of the dissolved salt and has the volume of 600 mL.


Thus you have these two equations


    x + y = 600    milliliters           (1)    (the total volume)

    {{{(0.05x + 0.11y)/600}}} = 0.07.                 (2)    (the resulting mixture concentration)



From equation  (1), express  x = 600 - y.  Substitute it into equation (2) and multiply both sides of this equation by 600. 
You will get


    0.05*(600-y) + 0.11y = 0.07*600.


From the last equation express y and calculate


    y = {{{(0.07*600 - 0.05*600)/(0.11-0.05)}}} = 200 mL of the 11% mixture are needed.


Then from equation (1),  x = 600 - 200 = 400 mL of the 5% mixture are needed.


<U>Answer</U>. 200 mL of the 11% mixture  and  400 mL of the 5% mixture are  needed.


<U>Check</U>.  {{{(0.11*200 + 0.05*400)/600}}} = 0.07 = 7%.   ! Correct concentration !
</pre>

The problem is just solved.

I used 2-equation setup and the Substitution method.


There are other solution methods, too.


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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>

&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.