Julian and Gillian has some money each. If Gillian gives Julian $12, he will have 3 times as much money as her. If Julian gives Gillian $11, he will have the same amount of money as her. How much money does each person have respectively?

1. Julian?
2. Gillian?

	Case 1		Case 2
	Julian	Gillian	Julian	Gillian
Before	3 u - 12	1 u + 12	2 u + 11	2 u - 11
Change	+ 12	- 12	- 11	+ 11
After	3 u	1 u	2 u	2 u

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

Total amount that Julian and Gillian have in the end for both cases
= 3 u + 1 u
= 4 u

Amount that Julian and Gillian each has in the end in Case 2
= 4 u ÷ 2
= 2 u

The amount that Julian has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 11
3 u - 2 u = 11 + 12

1 u = 23

Amount that Julian has
= 2 u + 11
= 2 x 23 + 11
= 46 + 11
= $57

(b)
Amount that Gillian has
= 1 u + 12
= 23 + 12
= $35

Answer(s): (a) $57; (b) $35