x = gallons of 10%
3-x = gallons of 40%
amount of juice in 10% = .1x
amount of juice in 40% = .4(3-x)
Final amount of juice is 3 gallons at 20% = .2 (3)
the ingredients = final
.1x + .4(3-x) = .2 (3)
-.3x + 1.2 = .6
-.3x = -.6
x = 2 2 gals of 10% 3-2 = 1 gal of 40%