Answer:
3
Step-by-step explanation:
Assume that the total amount of alcohol at the end is x, and that you are adding y gallons to the mixture. We have 6+y=x, and x*0.4 (40% of x) = y+current amount of alcohol. The current amount of alcohol is 10%*6, or 0.6 gallons, so x*0.4 = y+0.6. Solving for y, we have
x-6=y (from 6+y=x),
and putting that into our second equation, we have
x*0.4 = (x-6)+0.6, so
x*0.4 = x-5.4, and subtracting x from both sides, we get
-0.6*x = -5.4, and dividing both sides by -0.6, we get that
x=9
Thus, y=x-6=3, our answer
