If Shiyun gives Ben $19, the amount of money she has will be 25% of his. If Ben gives Shiyun $38, he will have the same amount of money as her. How much money did each of them have?
(a) Ben
(b) Shiyun

	Case 1		Case 2
	Ben	Shiyun	Ben	Shiyun
Before	4 u - 19	1 u + 19	2.5 u + 38	2.5 u - 38
Change	+ 19	- 19	- 38	+ 38
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 19 = 2.5 u + 38
4 u - 2.5 u = 38 + 19
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Ben has
= 4 u - 19
= 4 x 38 - 19
= 152 - 19
= $133 

(b)
Amount that Shiyun has
= 1 u + 19
= 1 x 38 + 19
= 38 + 19
= $57

Answer(s): (a) $133; (b) $57