If Eva gives Simon $31, the amount of money she has will be 30% of his. If Simon gives Eva $39, he will have the same amount of money as her. How much money did each of them have?
(a) Simon
(b) Eva

	Case 1		Case 2
	Simon	Eva	Simon	Eva
Before	10 u - 31	3 u + 31	6.5 u + 39	6.5 u - 39
Change	+ 31	- 31	- 39	+ 39
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Simon gives to Eva, there is an internal transfer of money from Simon to Eva. 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 Eva and Simon have
= 10 u + 3 u
= 13 u

Amount that Eva and Simon each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 31 = 6.5 u + 39
10 u - 6.5 u = 39 + 31
3.5 u = 70 

1 u = 70 ÷ 3.5 = 20

Amount that Simon has
= 10 u - 31
= 10 x 20 - 31
= 200 - 31
= $169 

(b)
Amount that Eva has
= 3 u + 31
= 3 x 20 + 31
= 60 + 31
= $91

Answer(s): (a) $169; (b) $91