Answer:
17
Step-by-step explanation:
Let a,b,c,d,x represent the five integers in Ascending order.
Given;
The sum of five different positive integers is 320
a+b+c+d+x = 320 .......1
The sum of the greatest three integers in this set is 283
c+d+x = 283 .....2
The sum of the greatest and least integers is 119
a+x = 119 ......3
For the largest possible value;
From equation 3, if a is as low as 1,
x = 119-1 = 118
x = 118
For the least possible value;
Subtract equation 2 from 1
a+b = 320-283 = 37
We know that a cannot be higher than b, so the highest possible value of a is;
a = 37-b
a = 37- 19 = 37-19
a = 18
Substituting into equation 3
x = 119-18 = 101
Difference;
∆x = 118-101 = 17
