Recipes and Adjusting Ingredient Amounts

Date: 04/20/2005 at 17:00:48
From: Sandie
Subject: breaking down a recipe

In a recipe, 5 1/2 cups of coconut uses 14 ounces of milk, but I only
have 4 cups of coconut, so how many ounces of milk do I use?

Date: 04/21/2005 at 11:52:28
From: Doctor Wilko
Subject: Re: breaking down a recipe

Hi Sandie,

Thanks for writing to Dr. Math!  I want to give you two different ways
to approach this problem. 

Method One: Think about Ounces per Cup

Your recipe says you need to mix 14 oz of milk with 5.5 cups of 
coconut, right?  So my question is, "How many ounces of milk do you 
mix with one cup of coconut?"  Break it down by dividing the 14 ounces
by the 5.5 cups:

   14 oz
  ------- is about 2.54 oz of milk per cup of coconut
   5.5 c

So, if you have four cups of coconut, then you'd mix

  (2.54 oz of milk per cup of coconut) * (4 c of coconut) =

   2.54 * 4 or about 10.16 oz of milk
 
Method Two: Set Up a Proportion

You want to keep the ingredients in the same amount relative to each
other, or the same ratio.  Two equal ratios make a proportion.

You can set this up as follows:

    14 oz Milk          ? oz Milk
 ----------------- = ---------------
  5.5 cups coconut    4 cups coconut

In any proportion, if you multiply the top of one ratio times the
bottom of the other, you will get the same answer in both directions.
So we know that:

  (14)*(4) = (5.5)*(?)

  56 = (5.5)*(?)

Divide 56 by 5.5 to see what the (?) must be, just as if you had
something like 8 = (4)*(?).

  56/5.5 = 10.18 ounces of milk

  10.18 oz is approximately equal to 10 oz + 1 Tsp

You should mix (10 oz + 1 Tsp) of milk with your four ounces of 
coconut to keep the recipe in the right proportion!

The difference from the answer above (10.16) is due to rounding, but 
the point is that you need just over 10 oz of milk to keep the same 
consistency or proportion of the original recipe.  

If you'd like to see more about proportions, check these links from 
our archives:

  Comparing Ratios to Form Proportions
    http://mathforum.org/library/drmath/view/64554.html 

  Ratios and Proportions in Everyday Life
    http://mathforum.org/library/drmath/view/60681.html 

Another way to think about it is, no matter what size recipe you're 
making or how much coconut you have, if you mix about two and a half 
ounces of milk for every cup of coconut, you'll keep the recipe in 
proper proportion.

Does this help?  Please write back if you have more questions.

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