Fractions of a Cup

Date: 04/15/2003 at 22:30:06
From: Kirstie
Subject: Reducing many cups to one cup

If you made 1 cup of mix, how much water and how much concentrate 
would you need?                  

   MIX W
3 cups concentrate
4 cups cold water

I can't figure out how to reduce many cups to 1 cup. I thought it was 
1/4 cup water and 1/3 cup concentrate, but I don't think that's right.

Date: 04/16/2003 at 14:16:04
From: Doctor Ian
Subject: Re: Reducing many cups to one cup

Hi Kirstie,

One way you can check your answer is this:  The quantities would have
to add up to 1 cup.  Do you see why? 

Let's try that:

  1/4 + 1/3 = 3/12 + 4/12 

            = 7/12

which is less than a cup.  So we need to find a different answer. 

Let's say you make all 7 cups of the mix.  Then you have 7 cups of
mix, which contains 3 cups of concentrate, and 4 cups of water. 

  +-------------+
  |             |  <-- concentrate
  +-------------+
  |             |  <-- concentrate
  +-------------+
  |             |  <-- concentrate
  +-------------+
  |             |  <-- water
  +-------------+
  |             |  <-- water
  +-------------+
  |             |  <-- water
  +-------------+
  |             |  <-- water
  +-------------+


Now to get 1 cup, you're going to divide the mix into 7 equal parts:

  +-------------+
  |c|c|c|c|c|c|c|           Each 'c' is 1/7 of a cup
  |c|c|c|c|c|c|c|
  |c|c|c|c|c|c|c|
  +-------------+
  |w|w|w|w|w|w|w|           Each 'w' is 1/7 of a cup
  |w|w|w|w|w|w|w|
  |w|w|w|w|w|w|w|
  |w|w|w|w|w|w|w|
  +-------------+

And keep one of them:

  +-+
  |c|
  |c|
  |c|
  +-+
  |w|
  |w|
  |w|
  |w|
  +-+

So how much of each (concentrate or water) do you have? 

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/