SOLUTION: A first aid treatment for extensive burn calls for a solution which is 5% baking soda. How much ounces of water must be added to 12 ounces of a 15% solution of baking soda so that

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Question 1160379: A first aid treatment for extensive burn calls for a solution which is 5% baking soda. How much ounces of water must be added to 12 ounces of a 15% solution of baking soda so that the new solution will only be 5% baking soda?
Answer by greenestamps(13367) (Show Source):
You can put this solution on YOUR website!

(1) First, a common sense informal solution....

You want the concentration of the solution to be cut to one-third of the current 15%, to 5%.

Since what you are adding is water (no baking soda), that means the solution you start with needs to be one-third of the final mixture.

So the water you are adding is two-thirds of the final mixture; since that is twice as much as what you started with, the amount of water you need to add is 12*2 = 24 ounces.

(2) A formal algebraic solution, using the standard method....

You are combining 12 ounces of 15% baking soda with x ounces of 0% baking soda (water) to get (12+x) ounces of 5% baking soda:

(3) And finally, another method for solving mixture problems like this without formal algebra. This method is the fastest and easiest, if you understand how to use it.

Think of it this way:
(a) you are starting at 15% baking soda; by adding water (0% baking soda) you are heading towards 0%; but you stop when you get to 5%
(b) 5% is 2/3 of the way from 15% to 0%
(c) therefore, 2/3 of the mixture is what you are adding

So the original 12 ounces of 15% baking soda is 1/3 of the mixture; that means the water you are adding is 2/3 of the mixture, which is 24 ounces.