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

let the 3 numbers be x, y, and z from smallest to largest

x+y+z = 18

z-x = 26/5
z = 26/5 + x

into the first:
x + y + 26/5 + x = 18
2x+y = 64/5
y = 64/5 - 2x
= (64-10x)/5

but x, y, and z are to be mixed numbers, that is, they must all be greater than 1
so to find y, 64-10x > 5
-10x > -59
x < 5.9
so we need 1 < x < 5.9

so pick value of x within that domain, say
x = 4
then y = (64-40)/5 = 24/5
and z = 26/5 + 24/5 = 10
one possible answer is
x= 4/1, y=24/5, z=10/1

another:
let x = 5/3
y = (64-50/3)/5 = 142/15
z = 26/5 + 5/3 = 103/15

check:
sum = 5/3 + 142/15 + 103/15 = 18
difference 103/15-5/3 = 26/5 = 5 1/5

so you can pick any x you want within the given domain, and find the corresponding triple.
There will be an infinite number of such possible triples