Dearest tutors, can you help me regarding my problem? thank you for that..
3. How much pure alcohol must be added to 8 quarts of a 20% solution of alcohol
produce a 40% solution?
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Let the answer be x.

First we figure the amount of LIQUID we'll have. Then we figure the amount of
ALCOHOL we'll have.

We have 8 quarts of LIQUID to start with and we add x quarts of LIQUID, so we
end up with 8+x quarts of LIQUID.  

Now we figure the amount of ALCOHOL.

Only 20% of the 8 quarts we start with is ALCOHOL. 20% of 8 quarts is 1.6
quarts.  So we have 1.6 quarts of ALCOHOL to start with, and we add x quarts
of ALCOHOL, so we end up with 1.6+x quarts of ALCOHOL.

Now we reason that the 1.6+x quarts of ALCOHOL we end up with must be 40%
of the 8+x quarts of LIQUID we end up with, so we put that into an equation:

   1.6+x quarts of ALCOHOL EQUALS 40% of 8+x quarts of LIQUID, or

               1.6+x = .40(8+x)

solve that and you'll get x = 8/3 or 2 2/3 quarts.  If you can't solve that,
post again and we'll help you solve it.

Edwin