If Xuan gives Fabian $27, the amount of money she has will be 10% of his. If Fabian gives Xuan $63, he will have the same amount of money as her. How much money did each of them have?
(a) Fabian
(b) Xuan

	Case 1		Case 2
	Fabian	Xuan	Fabian	Xuan
Before	10 u - 27	1 u + 27	5.5 u + 63	5.5 u - 63
Change	+ 27	- 27	- 63	+ 63
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

In Case 1, when Xuan gives to Fabian, there is an internal transfer of money from Xuan to Fabian.  The total amount that both have remains the same.

In Case 2, when Fabian gives to Xuan, there is an internal transfer of money from Fabian to Xuan. The total amount that both have remains the same.

The total amount that both have in Case 1 and Case 2 are the same.

Total amount that Xuan and Fabian have
= 10 u + 1 u
= 11 u

Amount that Xuan and Fabian each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

Amount that Fabian has at first is the same in Case 1 and Case 2.

10 u - 27 = 5.5 u + 63
10 u - 5.5 u = 63 + 27
4.5 u = 90 

1 u = 90 ÷ 4.5 = 20

Amount that Fabian has
= 10 u - 27
= 10 x 20 - 27
= 200 - 27
= $173 

(b)
Amount that Xuan has
= 1 u + 27
= 1 x 20 + 27
= 20 + 27
= $47

Answer(s): (a) $173; (b) $47