George and Cathy has some money each. If Cathy gives George $17, he will have 5 times as much money as her. If George gives Cathy $10, he will have the same amount of money as her. How much money does each person have respectively?

1. George?
2. Cathy?

	Case 1		Case 2
	George	Cathy	George	Cathy
Before	5 u - 17	1 u + 17	3 u + 10	3 u - 10
Change	+ 17	- 17	- 10	+ 10
After	5 u	1 u	3 u	3 u

(a)
If Cathy gives George some money or George gives Cathy some money, the total amount of money remains the same.  

Total amount that George and Cathy have in the end for both cases
= 5 u + 1 u
= 6 u

Amount that George and Cathy each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that George has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 10
5 u - 3 u = 10 + 17

1 u = 27

Amount that George has
= 3 u + 10
= 3 x 27 + 10
= 81 + 10
= $91

(b)
Amount that Cathy has
= 1 u + 17
= 27 + 17
= $44

Answer(s): (a) $91; (b) $44