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

1. John?
2. Joelle?

	Case 1		Case 2
	John	Joelle	John	Joelle
Before	5 u - 10	1 u + 10	3 u + 17	3 u - 17
Change	+ 10	- 10	- 17	+ 17
After	5 u	1 u	3 u	3 u

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

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

Amount that John and Joelle each has in the end in Case 2
= 6 u ÷ 2
= 3 u

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

1 u = 27

Amount that John has
= 3 u + 17
= 3 x 27 + 17
= 81 + 17
= $98

(b)
Amount that Joelle has
= 1 u + 10
= 27 + 10
= $37

Answer(s): (a) $98; (b) $37