Question 353721
Let x=amount that was drawn each time

After this amount is drawn and replaced by water the percent of pure alcohol remaining in the mixture is (49-x)/49; after we draw x amount from the mixture again, the amount of pure alcohol is ((49-x)/49)*(49-x) and we are told that this equals 36 gal.  Soooo our equation to solve is:
((49-x)/49)*(49-x)=36  multiply each side by 49
(49-x)^2=1764  take the square root of both sides (we will only deal in positive #'s)
49-x=42 or
x=7 gal ----amount that was drawn each time
CK
((49-7)/49)*(49-7)=36
36=36

Hope this helps---ptaylor