SOLUTION: One hundred liters of a solution was available, but the solution was 65% alcohol. Barry needed a solution which was 50% alcohol. How many liters of alcohol had to be extracted so

Question 71399: One hundred liters of a solution was available, but the solution was 65% alcohol. Barry needed a solution which was 50% alcohol. How many liters of alcohol had to be extracted so that the solution would be 50% alcohol?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The problem tells you that Barry has 100 liters of solution. 65% of that amount (or 65
liters) is alcohol. The rest (35 liters) is the solvent.
.
To get a 50% mixture, Barry starts removing only alcohol. But he removes no solvent.
The 35 liters of solvent is always there. So Barry must get the alcohol down to 35 liters.
That way there will be 35 liters of alcohol to match the 35 liters of solvent for the 50%
mixture he is looking for. He started with 65 liters of alcohol in the mixture, and to
get down to 35 liters he will have to extract 30 liters of alcohol. And when he is done
there will now be 70 liters of mixture consisting of 35 liters of alcohol and 35 liters
of solvent.
.
Sometimes its easier to think your way through a problem than to try to find an equation that
you just plug numbers into and hope for the best. Hope this gives you an appreciation
for the logic of mathematical thought processes.
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