Question 1201150
.
A certain automobile cooling system contains 12.0 L of coolant that is 15% antifreeze.
How many liters of mixture must be removed so that, when it is replaced with pure antifreeze, 
a mixture of 23% antifreeze will result?
~~~~~~~~~~~~~~~~


<pre>
Let x be the volume of the mixture, in liters, which should be removed and replaced 
by the pure antifreeze.


Then the remaining volume of the mixture is (12-x) liters, anf it contains 
0.15*(12-x) liters of the pure antifreeze.


After adding x liters of the pure antifreeze, the volume of the pure antifreeze in
the updated mixture is  (0.15*(12-x)+x) liters.


The total volume of the updated mixtures remains the same 12 liters.


So, the concentration equation is

    {{{(0.15*(12-x) + x)/12}}} = 0.23.


Simplify and find x

    0.15*(12-x) + x = 0.23*12

    1.8 - 0.15x + x = 2.76

          0.85x     = 2.76 - 1.8

          0.85x     =    0.96

              x     =    0.96/0.85 =  1.129 liters  (rounded).    <U>ANSWER</U>

<U>CHECK</U>  the new concentration  {{{(0.15*(12-1.129) + 1.129)/12}}} = 0.22997... (correct).
</pre>

Solved.


-------------------


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/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>


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.