SOLUTION: A vat contains 27 gallons of water and 9 gallons of acetic acid. How many gallons of water must be evaporated if the resulting solution is to be 40% acetic acid?

Question 641384: A vat contains 27 gallons of water and 9 gallons of acetic acid. How many gallons of water must be evaporated if the resulting solution is to be 40% acetic acid?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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