Question 559646
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The "draining off" and "replacing" in the problem only complicates the process of solving the problem.  Essentially, you are simply mixing a 25% antifreeze solution with a 100% antifreeze solution to obtain 16 quarts of 40% antifreeze.<br>
The question asks for the amount of pure antifreeze to be used.  So<br>
x = quarts of 100% antifreeze
16-x = quarts of 25% antifreeze<br>
The mixture is 40% antifreeze:<br>
{{{1.00(x)+.25(16-x)=.40(16)}}}<br>
I leave it to you to solve the problem by that formal algebraic method.  As shown the the other tutors, the answer is 3.2 quarts.<br>
Here is an informal method that can be used to solve any 2-part mixture problem like this.<br>
The three percentages in the problem are 25, 40, and 100.  Picture (in your mind, or on paper if needed) those three percentages on a number line.  Then observe/calculate that 40 is 15/75 = 1/5 of the way from 25 to 100.  That means 1/5 of the mixture is the 100% antifreeze.<br>
1/5 of 16 quarts is 3.2 quarts.<br>
ANSWER: 3.2 quarts<br>