Question 1203015
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I will show several ways to solve the problem.  Since having more tools at your disposal makes you a better problem solver, I would recommend looking at and trying to understand all of them.<br>
(1) 20% of 20 liters is 4 liters; since you are adding water (0% salt) you will still have 4 liters of salt after adding the water.  12.5% as a fraction is 1/8, so the 4 liters of salt you have must be 1/8 of the final salt solution.  That means the final solution is 32 liters; and that means you added 12 liters of water.<br>
ANSWER: 12 liters<br>
(2) Traditional algebra...<br>
You are mixing 20 liters of 20% salt to x liters of 0% salt to end up with (20+x) liters of 12.5% salt:<br>
{{{.20(20)+0(x)=.125(20+x)}}}
{{{4=(1/8)(20+x)}}}
{{{32=20+x}}}
{{{x=12}}}<br>
ANSWER: 12 liters<br>
(3) Alligation (yes, with an "i") -- this method is apparently taught in pharmacology.<br>
You asked for a diagram.  This method in fact uses a diagram....<br>
Here is the diagram for your problem:<br><pre>

    20      12.5
       12.5
     0       7.5</pre>
The "20" and "0" in the first column are the percentages of salt in the two ingredients.
The "12.5" in the middle of the diagram is the percentage of the mixture.
The "12.5" and "7.5" in the third column are the differences -- calculated diagonally -- between the numbers in the first column and the number in the second column: 12.5 is the difference between 0 and 12.5, and 7.5 is the difference between 20 and 12.5.
The two numbers in the third column give you the RATIO in which the two ingredients must be mixed.  In this problem, that ratio is 12.5:7.5 = 5:3.  So you need 5 parts of the 20% salt solution to 3 parts of water.<br>
Given that there are 20 liters of the 20% salt solution, find the number of liters of water using a proportion:<br>
5:3 = 20:x
60 = 5x
x = 12<br>
ANSWER: 12 liters<br>
(4) Finally, here is what I think is the easiest and fastest way to solve any 2-part mixture problem like this.  It is closely related to the previous method, but to me the calculations are much simpler.<br>
You are starting with a 20% salt solution and adding 0% salt until you have a mixture that is 12.5% salt.  Think of that as "starting at 20 and walking towards 0, stopping when you get to 12.5".<br>
Mentally, or using a number line if it helps, observe/calculate that 12.5 is 3/8 of the way from 20 to 0.<br>
That means 3/8 of the final mixture is what you are adding. (You started at 20 and walked towards 0, but you stopped when you were only 3/8 of the way there; so 3/8 of the mixture is what you are adding.)<br>
Since 3/8 of the mixture is the water you are adding, the original 20 liters of 20% salt solution is 5/8 of the mixture.<br>
Then, similar to the previous method, you have a proportion to solve: knowing that 5/8 of the mixture is 20 liters; you know 3/8 of the mixture which is the water you are adding is 12 liters.<br>
ANSWER: 12 liters<br>