Question 641384
Let x=amount of water that needs to be evaporated in order to get a solution that is 40% acetic acid
Initially the vat contains 27+9=36 gal of a solution of which 9 gal is pure acetic acid(9/36 =1/4 or 25% acetic acid)

Now we know that he amount of pure acetic acid that exists before the evaporation takes place (0.25*36=9 gal) has to equal the amount of pure acetic acid that exists after x amount of water is evaporated (0.40(36-x)). Soooooo
9=0.40(36-x) simplify
9=14.4-0.40x subtract 14.4 from each side
-5.4=-0.40x
x=13.5 gal--amount of water that needs to be evaporated

CK
9=0.40(36-13.5)=0.40*22.5
9=9

Hope this helps---ptaylor