Question

Find three mixed numbers so that the sum is 18 and the difference between the greatest number and the least number is 5 1/5.

Answer 1

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.

So, pick any value for y that you want, up to 32/5, which would make z=0.