Associated Topics || Dr. Math Home || Search Dr. Math

### 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

```
Associated Topics:
Middle School Algebra
Middle School Ratio and Proportion

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search