Question

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