lets fix a value of x1, say 5. How many solutions are left?

The new equation is x2+x3=100-5

Which has 96 solutions. These correspond to x2 taking every value between 0 and 95, and x3=95-x2.

Generalising, we could fix x1 at any value between 0 and 100.

So the number of solutions is:

Can you finish from there?