suppose y=0. That means
x+z = 18
x-z = 26/5
x = 58/5
z = 32/5
So, the largest x can be is 58/5
Now, suppose we toss in y. If we subtract y/2 from both x and z, then the difference between x and z is still 26/5, and the sum is
(x-y/2) + y + (z-y/2) = x+z = 18
For example, if y = 4,
x = 48/5
y = 20/5
z = 22/5
x-z is still 26/5, and the sum is still 18.
