Question 1160379
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(1) First, a common sense informal solution....<br>
You want the concentration of the solution to be cut to one-third of the current 15%, to 5%.<br>
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.<br>
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.<br>
(2) A formal algebraic solution, using the standard method....<br>
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:<br>
{{{.15(12)+0(x) = .05(12+x)}}}
{{{1.8 = 0.6+.05x}}}
{{{1.2 = .05x}}}
{{{x = 1.2/.05 = 24}}}<br>
(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.<br>
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<br>
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.<br>