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

1. Ben?
2. Raeann?

	Case 1		Case 2
	Ben	Raeann	Ben	Raeann
Before	7 u - 10	1 u + 10	4 u + 16	4 u - 16
Change	+ 10	- 10	- 16	+ 16
After	7 u	1 u	4 u	4 u

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

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

Amount that Ben and Raeann each has in the end in Case 2
= 8 u ÷ 2
= 4 u

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

1 u = 26

Amount that Ben has
= 4 u + 16
= 4 x 26 + 16
= 104 + 16
= $120

(b)
Amount that Raeann has
= 1 u + 10
= 26 + 10
= $36

Answer(s): (a) $120; (b) $36