Valen and Marion has some money each. If Marion gives Valen $10, he will have 3 times as much money as her. If Valen gives Marion $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Valen?
2. Marion?

	Case 1		Case 2
	Valen	Marion	Valen	Marion
Before	3 u - 10	1 u + 10	2 u + 19	2 u - 19
Change	+ 10	- 10	- 19	+ 19
After	3 u	1 u	2 u	2 u

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

Total amount that Valen and Marion have in the end for both cases
= 3 u + 1 u
= 4 u

Amount that Valen and Marion each has in the end in Case 2
= 4 u ÷ 2
= 2 u

The amount that Valen has at first in Case 1 and Case 2 is the same.
3 u - 10 = 2 u + 19
3 u - 2 u = 19 + 10

1 u = 29

Amount that Valen has
= 2 u + 19
= 2 x 29 + 19
= 58 + 19
= $77

(b)
Amount that Marion has
= 1 u + 10
= 29 + 10
= $39

Answer(s): (a) $77; (b) $39