The Ratio of Water to Wine
Date: 10/22/95 at 0:4:6 From: Anonymous Subject: Ratios Hi , I need help with this question and I don't know where to begin!!. A cask is filled with 45 gallons of wine . Nine gallons are removed and the cask is refilled with water. The nine gallons of the mixture are removed and the cask is refilled with water again. What is the ratio of water to wine in the final mixture?
Date: 10/23/95 at 11:44:35 From: Doctor Ken Subject: Re: Ratios Hello! Here's how I would approach the problem. You know what the mixture is right after you do the first water replacement: there are 36 gallons of wine and 9 gallons of water. So what is the ratio of wine to water in the flask at that point? It's 36/9 = 4/1, so assuming a homogenous mixture, in every 5 parts of liquid there are 4 parts wine and 1 part water. So 4/5 of every volume that you remove is wine, and the rest is water. Now you can figure out how much of the stuff you remove in the second round is actually wine, and then you can figure out how much is left in the cask. Good luck! -Doctor Ken, The Geometry Forum
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