Dylan and Xylia has some money each. If Xylia gives Dylan $16, he will have 7 times as much money as her. If Dylan gives Xylia $10, he will have the same amount of money as her. How much money does each person have respectively?

1. Dylan?
2. Xylia?

	Case 1		Case 2
	Dylan	Xylia	Dylan	Xylia
Before	7 u - 16	1 u + 16	4 u + 10	4 u - 10
Change	+ 16	- 16	- 10	+ 10
After	7 u	1 u	4 u	4 u

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

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

Amount that Dylan and Xylia each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Dylan has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 10
7 u - 4 u = 10 + 16

1 u = 26

Amount that Dylan has
= 4 u + 10
= 4 x 26 + 10
= 104 + 10
= $114

(b)
Amount that Xylia has
= 1 u + 16
= 26 + 16
= $42

Answer(s): (a) $114; (b) $42