If Xuan gives Liam $14, the amount of money she has will be 10% of his. If Liam gives Xuan $166, he will have the same amount of money as her. How much money did each of them have?
(a) Liam
(b) Xuan

	Case 1		Case 2
	Liam	Xuan	Liam	Xuan
Before	10 u - 14	1 u + 14	5.5 u + 166	5.5 u - 166
Change	+ 14	- 14	- 166	+ 166
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Liam gives to Xuan, there is an internal transfer of money from Liam 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 Liam have
= 10 u + 1 u
= 11 u

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

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

10 u - 14 = 5.5 u + 166
10 u - 5.5 u = 166 + 14
4.5 u = 180 

1 u = 180 ÷ 4.5 = 40

Amount that Liam has
= 10 u - 14
= 10 x 40 - 14
= 400 - 14
= $386 

(b)
Amount that Xuan has
= 1 u + 14
= 1 x 40 + 14
= 40 + 14
= $54

Answer(s): (a) $386; (b) $54