Question 1091613
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<pre>
Let x be the volume of the pure antifreeze under the question, in quarts.

8 quarts of the 50% antifreeze solution contain 0.5*8 quarts of the pure antifreeze.

When we add x quarts of the pure antifreeze, the amount of pure antifreeze becomes x + 0.5*8 quarts.

The total volume of liquid solution becomes (x+8) quarts.

Therefore, the antifreeze concentration after adding becomes  {{{(x + 0.5*8)/(x+8)}}}.


According to the condition, it must be 60% = 0.6. It gives you an equation

{{{(x + 0.5*8)/(x+8)}}} = 0.6.


To solve it, first multiply both sides by (x+8). You will get

x + 4 = 0.6*(x+8),   or

x + 4 = 0.6x + 4.8  ====>  x - 0.6x = 4.8 - 4  ====>  0.4x = 0.8  ====>  x = {{{0.8/0.4}}} = 2.


<U>Answer</U>. 2 quarts of the pure antifreeze must be added.
</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>

in this site.


Among them, find the lesson on antifreeze marked by (*).
Read these lessons and become an expert in solving 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>".