If Winnie gives Ian $39, the amount of money she has will be 40% of his. If Ian gives Winnie $3, he will have the same amount of money as her. How much money did each of them have?
(a) Ian
(b) Winnie

	Case 1		Case 2
	Ian	Winnie	Ian	Winnie
Before	5 u - 39	2 u + 39	3.5 u + 3	3.5 u - 3
Change	+ 39	- 39	- 3	+ 3
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Ian gives to Winnie, there is an internal transfer of money from Ian to Winnie. 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 Winnie and Ian have
= 5 u + 2 u
= 7 u

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

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

5 u - 39 = 3.5 u + 3
5 u - 3.5 u = 3 + 39
1.5 u = 42 

1 u = 42 ÷ 1.5 = 28

Amount that Ian has
= 5 u - 39
= 5 x 28 - 39
= 140 - 39
= $101 

(b)
Amount that Winnie has
= 2 u + 39
= 2 x 28 + 39
= 56 + 39
= $95

Answer(s): (a) $101; (b) $95