Jennifer has $400 more than Brian has.
J = B + 400

If she were to give Brian 20% of her money,
0.2J+B

then Brian would have 2/3 of the amount of money that Jennifer would then have.
2/3(0.8J) (0.8 means remaining amount)

How much money does Brian currently have (before exchanging money)?
B+0.2J=2/3(0.8J)
3B + 0.6J = 1.6J
3B = 1J

J = B + 400
3B - B = 400
2B = 400
B=200

Can we solve this by using smart numbers?

Here's one approach:

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

Jennifer has $400 more than Brian.
So, J = B + 400

If Jennifer were to give Brian 20% of her money, Brian would have 2/3 of the amount that Jennifer would then have.
20% of Jennifer's money = 1/5 of Jennifer's money = (1/5)J
So, if Jennifer gives Brian 1/5 of her money, then Jennifer now has (4/5)J dollars remaining, and Brian now has B + (1/5)J dollars

If Brian now has 2/3 of the amount that Jennifer now has, then: 2/3 of Jennifer's amount = Brian's amount
So, we can write: (2/3)(4/5)J = B + (1/5)J
Simplify, to get (8/15)J = B + (1/5)J
Multiply both sides by 15 to get: 8J = 15B + 3J
Rearrange: 5J = 15B
Divide both sides by 5 to get: J = 3B

We now have the system:
J = B + 400
J = 3B

When we solve it, we get B = 200 (as well as J = 600)

Answer: 200

Cheers,
Brent

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