Riordan and Jaslyn has some money each. If Jaslyn gives Riordan $13, he will have 5 times as much money as her. If Riordan gives Jaslyn $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Riordan?
2. Jaslyn?

	Case 1		Case 2
	Riordan	Jaslyn	Riordan	Jaslyn
Before	5 u - 13	1 u + 13	3 u + 19	3 u - 19
Change	+ 13	- 13	- 19	+ 19
After	5 u	1 u	3 u	3 u

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

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

Amount that Riordan and Jaslyn each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Riordan has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 19
5 u - 3 u = 19 + 13

1 u = 32

Amount that Riordan has
= 3 u + 19
= 3 x 32 + 19
= 96 + 19
= $115

(b)
Amount that Jaslyn has
= 1 u + 13
= 32 + 13
= $45

Answer(s): (a) $115; (b) $45