Michael and Jen has some money each. If Jen gives Michael $15, he will have 5 times as much money as her. If Michael gives Jen $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Michael?
2. Jen?

	Case 1		Case 2
	Michael	Jen	Michael	Jen
Before	5 u - 15	1 u + 15	3 u + 19	3 u - 19
Change	+ 15	- 15	- 19	+ 19
After	5 u	1 u	3 u	3 u

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

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

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

The amount that Michael has at first in Case 1 and Case 2 is the same.
5 u - 15 = 3 u + 19
5 u - 3 u = 19 + 15

1 u = 34

Amount that Michael has
= 3 u + 19
= 3 x 34 + 19
= 102 + 19
= $121

(b)
Amount that Jen has
= 1 u + 15
= 34 + 15
= $49

Answer(s): (a) $121; (b) $49