Question 751428
There are 3*0.4 = 1.2 gallons of pure antifreeze.


Let x = amount (in gallons) of pure antifreeze needed to add


If you add x gallons of pure antifreeze to 1.2 gallons of pure antifreeze, you'll have 1.2+x gallons of pure antifreeze


You are also adding x gallons of pure antifreeze to the 3 gallons of solution already there, so the total amount of solution is now 3+x gallons.


We can now say this


(1.2+x)/(3+x) = 0.5


since we want the percentage of pure antifreeze to total solution must be 50%


Now solve for x


(1.2+x)/(3+x) = 0.5


1.2+x = 0.5(3+x)


1.2+x = 1.5+0.5x


x = 1.5+0.5x-1.2


x-0.5x = 1.5-1.2


0.5x = 0.3


x = 0.3/0.5


x = 0.6


So you need to add <font color="red">0.6 gallons</font> of pure antifreeze to obtain 50% solution.