Question 1144544
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<pre>

Let x = the amount of the 70%  alcohol needed (in milliliters.

Then the amount of the resulting 65%  alcohol solution will be is (x+15) milliliters.


The amount of the "pure" alcohol in 15 mL of the 25% alcohol solution is 0.25*15 mL.

The amount of the "pure" alcohol in x mL of the 70% alcohol solution is 0.70*x mL.

The total amount of the "pure" alcohol in ingredients is the sum 0.25*15 + 0.70*x mL.


It should be equal to the amount of the "pure" alcohol in the mixture, which is 0.65*(x+15) ml.



So, your "pure alcohol" equation is 

   0.70*x + 0.25*15 = 0.65*(x+15).



Simplify and solve it for x:

    0.70x + 0.25*15 =  0.65x + 0.65*15,

    0.70x - 0.65x = 0.65*15 - 0.25*15,

    0.05x = 6,

    x = {{{6/0.05}}} = 120.

<U>Answer</U>. 120 mL of 70% alcohol solution are needed.


<U>Check</U>.  0.07*120 + 0.25*15 = 87.5 mL of the pure alcohol in ingredients, and

        0.65*(120+15) = 87.75 mL of the pure alcohol in the final mixture.   ! Precisely correct !
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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.