Question 1184008
.
How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 10% antifreeze 
to get a mixture that is 60% antifreeze? Use the six- step method
~~~~~~~~~~~~~~~~~~



            I don't know what the six-step method is; 
            therefore, I will solve the problem following to a standard procedure and common sense.



<pre>
100 gallons of 10% antifreeze contain 0.1*100 = 10 gallons of pure antifreeze.


If we add x gallons of the 70% of the antofreeze solution, the total liquid volume will be 100+x gallons,

and the content of antifreeze in it will be  10+0.7x  gallons.



Now, the concentration of the antifreeze in the new mixture is  C = {{{(10+0.7x)/(100+x)}}}  gallons of antifreeze
per gallon of the mixture.


It gives an equation to find x


    {{{(10+0.7x)/(100+x)}}} = 0.6.


To solve it, multiply both sides by (100+x) to get


    10+0.7x = 0.6*(100+x).


Simplify and find x


    10 + 0.7x = 60 + 0.6x

    0.7x - 0.6x = 60 - 10

        0.1x    =    50

         x      =    50/0.1 = 500.


<U>ANSWER</U>.  500 gallon of the 70% antifreeze solution should be added.


<U>CHECK</U>.   {{{(0.7*500 + 0.1*100)/(500+100)}}} = 0.6 = 60%.    ! Correct concentration !
</pre>

Solved.


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It is a standard and typical mixture problem.


In this site, there is a bunch of lessons, &nbsp;covering various types of mixture problems. &nbsp;See introductory lessons

&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/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>


Read them and become an expert in solution the 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 online textbook 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.