



 
Hi Roger. 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). Then 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) / (1p) 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,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 