x: volume of the 20% sol'n to be used in the mixture
y: vol. of the 80% sol'n to be used in the mixture
Then x+y must equal 30 gallons.
.20x: amt. of pure fertizer in the 20% sol'n
.80x: amt of pure fert. in the 80% sol'n
.60(x+y) = amt of pure fert in the 60% sol'n
Then:
.20x + .80y = .60(x+y) = .60(30)
Since x+y must equal 30, y=30-x, and
.20(x) + .80(30-x) = 18
.20x + 24 - .80x = 18
6 = .60x
x = 10
Use 10 gallons of the 20% solution and 20 gallons of the 80% solution.
The result will be 30 gallons of a 60% solution.
