If Shiyun gives Seth $34, the amount of money she has will be 25% of his. If Seth gives Shiyun $2, he will have the same amount of money as her. How much money did each of them have?
(a) Seth
(b) Shiyun

	Case 1		Case 2
	Seth	Shiyun	Seth	Shiyun
Before	4 u - 34	1 u + 34	2.5 u + 2	2.5 u - 2
Change	+ 34	- 34	- 2	+ 2
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 34 = 2.5 u + 2
4 u - 2.5 u = 2 + 34
1.5 u = 36 

1 u = 36 ÷ 1.5 = 24

Amount that Seth has
= 4 u - 34
= 4 x 24 - 34
= 96 - 34
= $62 

(b)
Amount that Shiyun has
= 1 u + 34
= 1 x 24 + 34
= 24 + 34
= $58

Answer(s): (a) $62; (b) $58