Here's one approach:

Let J = Jennifer's $
Let B = Brian's $

Jennifer has 60 dollars more than Brian.
So, J = B + 60

If Jennifer were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have.
If Jennifer were to give Brian 1/5 of her money, then Jennifer has (4/5)J dollars, and Brian has B + (1/5)J dollars

If Brian has 25% less than the amount that Jennifer has, then Brian's amount = 3/4 Jennifer's amount.
So, we can write: (3/4)(4/5)J = B + (1/5)J
Simplify, to get (3/5)J = B + (1/5)J
Multiply both sides by 5 to get: 3J = 5B + J
Rearrange: 2J = 5B

We now have the system:
J = B + 60
2J = 5B

When we solve it, we get J = 100 (as well as B = 40)

Answer: 100

Cheers,
Brent