So, 4 quarts of 10% antifreeze consists of .1 * 4 = .4 quarts of antifreeze.
x quarts of pure antifreeze consists of x quarts of antifreeze.
Mixing them together, the proportion of the solution that is antifreeze is given by
(.4 + q)/(4 + q).
We want to solve for a solution consisting of 50% antifreeze,
(.4 + q)/(4 + q) = .5 -> q = 3.2.
So, 3.2 quarts of pure antifreeze is required.
