Question 1153682
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If a formal algebraic solution is not required, here is a method that will get you to the answer to this and many similar problems with very little effort.<br>
Think of the problem as starting with 20% juice and adding 60% juice, stopping when the mixture is 50% juice.<br>
50% is 3/4 of the way from 20% to 60%.  (20 to 60 is 40; 20 to 50 is 30; 30/40 = 3/4.)<br>
That means 3/4 of the mixture must be the 60% juice you are adding.<br>
So the original 14 gallons of 20% juice is 1/4 of the mixture; that means the 3/4 of the mixture that is the added 60% juice is 3*14 = 42 gallons.<br>