Let X be the number of 12%-solution gallons added. 10-X will be the number of 20%-solution gallons.
0.14*10 = 0.20(10 -X) + 0.12 X
That is also the equation you wrote, and it says that the amount of solute in the mix is the sum of the amounts in the two mixed solutions.
Just solve it for X.
1.4 = 2 - 0.2 X + 0.12 X
0.6 = 0.08 X
X = 7.5 gallons
How does "How many gallons of a 12% indicator solution must be mixed with a 20% indicator solution to get 10 gal of a 14% solution?" turn into ".12x + .2(10+ -1x) = .14(10)"?? Please, I need to understand how it works! Thank you.
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