Caden and Jen has some money each. If Jen gives Caden $13, he will have 5 times as much money as her. If Caden gives Jen $15, he will have the same amount of money as her. How much money does each person have respectively?

1. Caden?
2. Jen?

	Case 1		Case 2
	Caden	Jen	Caden	Jen
Before	5 u - 13	1 u + 13	3 u + 15	3 u - 15
Change	+ 13	- 13	- 15	+ 15
After	5 u	1 u	3 u	3 u

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

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

Amount that Caden and Jen each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Caden has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 15
5 u - 3 u = 15 + 13

1 u = 28

Amount that Caden has
= 3 u + 15
= 3 x 28 + 15
= 84 + 15
= $99

(b)
Amount that Jen has
= 1 u + 13
= 28 + 13
= $41

Answer(s): (a) $99; (b) $41