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

1. Ben?
2. Xandra?

	Case 1		Case 2
	Ben	Xandra	Ben	Xandra
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 Xandra gives Ben some money or Ben gives Xandra some money, the total amount of money remains the same.  

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

Amount that Ben and Xandra each has in the end in Case 2
= 4 u ÷ 2
= 2 u

The amount that Ben 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 Ben has
= 2 u + 10
= 2 x 23 + 10
= 46 + 10
= $56

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

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