If Winnie gives Henry $24, the amount of money she has will be 40% of his. If Henry gives Winnie $9, he will have the same amount of money as her. How much money did each of them have?
(a) Henry
(b) Winnie

	Case 1		Case 2
	Henry	Winnie	Henry	Winnie
Before	5 u - 24	2 u + 24	3.5 u + 9	3.5 u - 9
Change	+ 24	- 24	- 9	+ 9
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 24 = 3.5 u + 9
5 u - 3.5 u = 9 + 24
1.5 u = 33 

1 u = 33 ÷ 1.5 = 22

Amount that Henry has
= 5 u - 24
= 5 x 22 - 24
= 110 - 24
= $86 

(b)
Amount that Winnie has
= 2 u + 24
= 2 x 22 + 24
= 44 + 24
= $68

Answer(s): (a) $86; (b) $68