At first I got a little confused trying to think of how much and what a quart is - i.e. the quart is a unit of volume (for either the imperial or United States customary units) equal to a quarter of a gallon (hence the name quart), two pints, or four cups ...
So I decided to just think of this as a bucket of solution and use numbers to solve the problem. Since the fractions were 3'rds and 8'ths, I pick 24 as the total amount in each bucket.
Two quarts containing 2⁄3 water and 1⁄3 formula:
water = 2/3 * 24 * 2 = 16 *2 = 32
..are mixed with three quarts containing 3⁄8 water and 5⁄8 formula:
water = 3/8 * 24 * 3 = 9 * 3 = 27
... approximately what percent of the combined five-quart mixture is water:
32 + 27 / (24*5) = 59 / 120 =~ 60/120 = 50%