If Shiyun gives Simon $40, the amount of money she has will be 40% of his. If Simon gives Shiyun $2, he will have the same amount of money as her. How much money did each of them have?
(a) Simon
(b) Shiyun

	Case 1		Case 2
	Simon	Shiyun	Simon	Shiyun
Before	5 u - 40	2 u + 40	3.5 u + 2	3.5 u - 2
Change	+ 40	- 40	- 2	+ 2
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 40 = 3.5 u + 2
5 u - 3.5 u = 2 + 40
1.5 u = 42 

1 u = 42 ÷ 1.5 = 28

Amount that Simon has
= 5 u - 40
= 5 x 28 - 40
= 140 - 40
= $100 

(b)
Amount that Shiyun has
= 2 u + 40
= 2 x 28 + 40
= 56 + 40
= $96

Answer(s): (a) $100; (b) $96