Date: Sat, 16 May 1998 11:07:01 -0700
Sender: Eddie
Subject: percentage question

I don't know what the level of this question is, but I am a 51-year old adult - not a student or a teacher. I'm looking for a formula or principle I can use to convert a given quantity of a 5% solution to a 4% solution, by adding water.

Example: If I have a recipe calling for 16 ounces of 4% vinegar (vinegar which has been diluted with water to a strength of 4%), and all I have on hand is 16 ounces of 5% vinegar, how much water should I add to decrease the strength to 4%, before measuring the 16 ounces to be used.

I'll appreciate any insight and help.

Thank you so much!


Pasadena, Calif.

  Hi Eddie,

I think that there are two ways to approach this problem.

  Since you have 16 ounces of liquid and 5% of it is vinegar, the amount of vinegar is 5% of 16 ounces, that is
0.05 x 16 = 0.8 ounces.
If you are going to add water to get T ounces of solution at 4% vinegar then the amount of vinegar, 0.8 ounces, remains constant so 4% of T ounces is 0.8 ounces. Thus
0.04 x T = 0.8
Hence T = 0.8/0.04 = 20 ounces. Thus of you add 4 ounces of water to 16 ounces of a 4% vinegar solution you will have 20 ounces of a 4% solution.
  Here is a second way to approach this problem.
  If you want 16 ounces of a 4% vinegar solution then you need
0.04 x 16 = 0.64 ounces of vinegar. Now ask yourself how many ounces of the 5% vinegar solution do you need for it to contain 0.64 ounces of pure vinegar. Suppose the answer is S ounces then 5% of S ounces is 0.64 ounces. That is
0.05 x S = 0.64, or
S = 0.64/0.05 = 12.8 ounces. Thus if you take 12.8 ounces of the 5% solution and add enought water to get 16 ounces then this 16 ounces will be 4% vinegar.
  I hope this helps,

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