Tom and Marion has some money each. If Marion gives Tom $13, he will have 3 times as much money as her. If Tom gives Marion $10, he will have the same amount of money as her. How much money does each person have respectively?

1. Tom?
2. Marion?

	Case 1		Case 2
	Tom	Marion	Tom	Marion
Before	3 u - 13	1 u + 13	2 u + 10	2 u - 10
Change	+ 13	- 13	- 10	+ 10
After	3 u	1 u	2 u	2 u

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

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

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

The amount that Tom has at first in Case 1 and Case 2 is the same.
3 u - 13 = 2 u + 10
3 u - 2 u = 10 + 13

1 u = 23

Amount that Tom has
= 2 u + 10
= 2 x 23 + 10
= 46 + 10
= $56

(b)
Amount that Marion has
= 1 u + 13
= 23 + 13
= $36

Answer(s): (a) $56; (b) $36