George and Mary has some money each. If Mary gives George $15, he will have 7 times as much money as her. If George gives Mary $14, he will have the same amount of money as her. How much money does each person have respectively?

1. George?
2. Mary?

	Case 1		Case 2
	George	Mary	George	Mary
Before	7 u - 15	1 u + 15	4 u + 14	4 u - 14
Change	+ 15	- 15	- 14	+ 14
After	7 u	1 u	4 u	4 u

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

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

Amount that George and Mary each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that George has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 14
7 u - 4 u = 14 + 15

1 u = 29

Amount that George has
= 4 u + 14
= 4 x 29 + 14
= 116 + 14
= $130

(b)
Amount that Mary has
= 1 u + 15
= 29 + 15
= $44

Answer(s): (a) $130; (b) $44