Question 960751
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The analysis by the other tutor is faulty....<br>
And if you evaluate the expression he shows for the amount of alcohol after the 8 drawings and replacements, it is more than 12 gallons -- which of course is nonsense.<br>
I did some ugly calculations for the first few drawings and replacements and noticed a clear pattern in the results; then I verified my calculations using an excel spreadsheet.<br>
Then I finally saw the simple explanation of the pattern I saw, and thus an easy path to the answer to the problem.<br>
Each time a drawing and replacement is made, 1/4 of the mixture is taken out and replaced with pure alcohol.  That means that with each drawing and replacement, the amount of water remaining gets reduced by a factor of 3/4.<br>
So after 8 drawings and replacements, the amount of water remaining is<br>
{{{12(3/4)^8}}} = 1.201355 gallons, to far more decimal places than practical.<br>
So the amount of alcohol in the radiator at that time is<br>
{{{12-1.201355}}} = 10.798645 gallons<br>