Sam and Jade has some money each. If Jade gives Sam $15, he will have 7 times as much money as her. If Sam gives Jade $18, he will have the same amount of money as her. How much money does each person have respectively?

1. Sam?
2. Jade?

	Case 1		Case 2
	Sam	Jade	Sam	Jade
Before	7 u - 15	1 u + 15	4 u + 18	4 u - 18
Change	+ 15	- 15	- 18	+ 18
After	7 u	1 u	4 u	4 u

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

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

Amount that Sam and Jade each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Sam has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 18
7 u - 4 u = 18 + 15

1 u = 33

Amount that Sam has
= 4 u + 18
= 4 x 33 + 18
= 132 + 18
= $150

(b)
Amount that Jade has
= 1 u + 15
= 33 + 15
= $48

Answer(s): (a) $150; (b) $48