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

1. Archie?
2. Roshel?

	Case 1		Case 2
	Archie	Roshel	Archie	Roshel
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 Roshel gives Archie some money or Archie gives Roshel some money, the total amount of money remains the same.  

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

Amount that Archie and Roshel each has in the end in Case 2
= 4 u ÷ 2
= 2 u

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

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

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