Let x = the number of gallons of 100% glycol you need and let p = the percentage concentration you need at the end (as a decimal: 20% = 0.20).
The ratio of these two is p.
p = [ 6800(0.17) + x(1.00) ] / (6800 + x)
To solve for x, we have:
p = (1156 + x) / (6800 + x)
x = (6800p - 1156) / (1-p)
So if you want 20%, then p is 0.20:
x = (6800(0.20) - 1156) / (1 - 0.20) = 255 gallons
You can solve this more generally. Let A be the quantity of the first liquid and a be the concentration of it. We will use up all of this first liquid.
Now let B be the quantity of the second liquid whose concentration is b. We will use as much of it as we need to make a mixture whose concentration is c (in between a and b, of course).
The total active ingredient in the mixture is
So c = (Aa + Ba) / (A + B)
And the unknown quantity B is therefore:
You can see that this is the same as your specific question because
the same as we arrived at earlier.
Hope this helps,
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