Gabriel and Elyse has some money each. If Elyse gives Gabriel $13, he will have 7 times as much money as her. If Gabriel gives Elyse $15, he will have the same amount of money as her. How much money does each person have respectively?

1. Gabriel?
2. Elyse?

	Case 1		Case 2
	Gabriel	Elyse	Gabriel	Elyse
Before	7 u - 13	1 u + 13	4 u + 15	4 u - 15
Change	+ 13	- 13	- 15	+ 15
After	7 u	1 u	4 u	4 u

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

Total amount that Gabriel and Elyse have in the end for both cases
= 7 u + 1 u
= 8 u

Amount that Gabriel and Elyse each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Gabriel has at first in Case 1 and Case 2 is the same.
7 u - 13 = 4 u + 15
7 u - 4 u = 15 + 13

1 u = 28

Amount that Gabriel has
= 4 u + 15
= 4 x 28 + 15
= 112 + 15
= $127

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

Answer(s): (a) $127; (b) $41