If Xuan gives Perry $14, the amount of money she has will be 40% of his. If Perry gives Xuan $19, he will have the same amount of money as her. How much money did each of them have?
(a) Perry
(b) Xuan

	Case 1		Case 2
	Perry	Xuan	Perry	Xuan
Before	5 u - 14	2 u + 14	3.5 u + 19	3.5 u - 19
Change	+ 14	- 14	- 19	+ 19
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Perry gives to Xuan, there is an internal transfer of money from Perry 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 Perry have
= 5 u + 2 u
= 7 u

Amount that Xuan and Perry each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

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

5 u - 14 = 3.5 u + 19
5 u - 3.5 u = 19 + 14
1.5 u = 33 

1 u = 33 ÷ 1.5 = 22

Amount that Perry has
= 5 u - 14
= 5 x 22 - 14
= 110 - 14
= $96 

(b)
Amount that Xuan has
= 2 u + 14
= 2 x 22 + 14
= 44 + 14
= $58

Answer(s): (a) $96; (b) $58