If Shiyun gives Vincent $39, the amount of money she has will be 25% of his. If Vincent gives Shiyun $33, he will have the same amount of money as her. How much money did each of them have?
(a) Vincent
(b) Shiyun

	Case 1		Case 2
	Vincent	Shiyun	Vincent	Shiyun
Before	4 u - 39	1 u + 39	2.5 u + 33	2.5 u - 33
Change	+ 39	- 39	- 33	+ 33
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Vincent gives to Shiyun, there is an internal transfer of money from Vincent to Shiyun. 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 Shiyun and Vincent have
= 4 u + 1 u
= 5 u

Amount that Shiyun and Vincent each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 39 = 2.5 u + 33
4 u - 2.5 u = 33 + 39
1.5 u = 72 

1 u = 72 ÷ 1.5 = 48

Amount that Vincent has
= 4 u - 39
= 4 x 48 - 39
= 192 - 39
= $153 

(b)
Amount that Shiyun has
= 1 u + 39
= 1 x 48 + 39
= 48 + 39
= $87

Answer(s): (a) $153; (b) $87