Question 1207753
.
The cooling system of a certain foreign-made car has a capacity of 15 liters. 
If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained 
and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze?


Let me see.


Mixture 1 + mixture 2 = total mixture 


15(0.40) + x = 0.60(x + 15)


Is this the correct set up? 
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Your setup equation is  INCORRECT.


This problem is a standard and typical mixture problem.


To see many similar problems solved with detailed explanations,  look into the lessons

&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> 

in this site. &nbsp;&nbsp;&nbsp;&nbsp;Learn the subject from there.



/\/\/\/\/\/\/\/\/\/\/\/



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Here I will show you very uncommon method of solution, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which allows to solve the problem practically &nbsp;MENTALLY.



<pre>
The amount of the pure antifreeze in 15 liters of the 40% mixture 
is 0.4*15 = 6 liters.


The amount of the pure antifreeze in 15 liters of the 60% mixture 
is 0.6*15 = 9 liters.


So, the original mixture contained 6 liters of the pure antifreeze;
the final mixture contains 9 liters of the pure antifreeze.


Now, Let V be the volume of the mixture to replace.


When we drain V liters of the 40% mixture, 0.4*V liters of the pure antifreeze go out.
We replace it with V liters of the pure antifreeze.


So, V should be 3 liters more than 0.4V, which means

    V - 0.4V = 3,  or  0.6V = 3,  hence  V = {{{3/0.6}}} = 5 liters.


At this point, the solution is complete, and we get the 


<U>ANSWER</U>.  5 liters of the of the original 40% mixture should be drained 

         and replaced by 5 liters of pure antifreeze.
</pre>

Solved in full and explained completely.



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Re-phrasing O'Henry, the famous American writer,


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The blind begin to walk and the dumb begin to see 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;when they receive such beautiful solutions to their problems.


There is nothing here except a mind game.