If Shiyun gives Seth $39, the amount of money she has will be 10% of his. If Seth gives Shiyun $114, 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	10 u - 39	1 u + 39	5.5 u + 114	5.5 u - 114
Change	+ 39	- 39	- 114	+ 114
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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
= 10 u + 1 u
= 11 u

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

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

10 u - 39 = 5.5 u + 114
10 u - 5.5 u = 114 + 39
4.5 u = 153 

1 u = 153 ÷ 4.5 = 34

Amount that Seth has
= 10 u - 39
= 10 x 34 - 39
= 340 - 39
= $301 

(b)
Amount that Shiyun has
= 1 u + 39
= 1 x 34 + 39
= 34 + 39
= $73

Answer(s): (a) $301; (b) $73