So Prize money of $500 is divided between Alan & Jim so that Alan receives $170 more than Jim How much does each receive

-----
Using one variable::
Let Jim have "x"
Then Alan has "x+170"
----
Equation:
x + x+170 = 500
2x = 330
x = $165 (Jim's share)
x+170 = $335

Good job

Each of them receives the following amounts:

Jim receives $165
Alan receives $335.