Math

I'm using  "e" for  "x"

Let   a < b < c < d < e

So we have......

a + b + c + d + e  = 320   (1)   

Where "a" is the smallest integer and "e" is the largest

And

c + d + e  =  283    (2)  

a + e  = 119     (3)

Sub (2) into (1)

a + b + 283  =  320

a + b  =  37

Let  a  =  1

Then.....as large as "e" can be is

1 + e  = 119

e  = 118

Let  a  = 36

Then......  a possibility for as small as "e" can be  is

36 + e  = 119

e  = 83

However     c < d < e

And  c + d + e  = 283

So....e will be minimized when  the sum of c and d are as large as possible

If      c  = d = e = 95

95 * 3  =  285....but  c and d  are < e.....so....c and d < 95  and  c < d

So....the largest that the sum of c and d can be  is  93 + 94  =   187

But.....

93 + 94 + 95   =  282   ......too small

Then e cannot be < 96  because  93 + 94 + 96  = 283

So.....as  small as e  can be  is  96   and as large as e can be  is  118

So.....the positive difference   between  the greatest positive value of  e   and the least positive value of e  is   118 - 96   =  22