SOLUTION: A farmer intends to sell a fifty gallon barrel of apple cider. He wants to dilute it so that it is one third water before he sells it. How many gallons of diluted cider will he be

Question 5964: A farmer intends to sell a fifty gallon barrel of apple cider. He wants to dilute it so that it is one third water before he sells it. How many gallons of diluted cider will he be able to get from the fifty gallon barrel?
( I keep getting 66.7 barrel: 1/3 of 50 barrel is 16.7, plus 50 is 66.7, but the answer is 75 barrels, would you explain the answer. Thanks)
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
He's got 50 gallons of "concentrate", right? So he needs to add water to it so that the resulting mixture will be 1/3 water, right?

Part I. How many gallons of water must he add to the 50 gallons so that the resulting mixture is 2/3 cider? Remember your basic fraction fact: part over whole. We'll set up a proportion here. Let's call w the amount of water you'll add to the mixture. Obviously, the whole mixture will be 50 + w because you'll be adding w gallons of water. So far, we have

We want the water to be 1/3 of the whole mixture, so

<---- We'll be solving for w

<----- We cross-multiplied.

<----- Subtract w from both sides

<----- So you must add 25 gallons of pure water then to dilute 50 gallons of cider concentrate. The question is asking you, though, for how much diluted "ready to sell" cider you'll end up with.

So you had 50 concentrate + 25 pure water = 75 diluted ready to sell.

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Your approach does actually makes sense but what that will do is actually divide your barrel into 3 parts, and each part will be equally 16.7 gallons. If you add 16.7 gallons of water, that will force your mixture to be 4 equal parts of 16.7 gallons. You'll then end up with 66.7 gallons of diluted cider, but it's going to be 1/4 water.
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