If Winnie gives Gabriel $15, the amount of money she has will be 80% of his. If Gabriel gives Winnie $9, he will have the same amount of money as her. How much money did each of them have?
(a) Gabriel
(b) Winnie

	Case 1		Case 2
	Gabriel	Winnie	Gabriel	Winnie
Before	5 u - 15	4 u + 15	4.5 u + 9	4.5 u - 9
Change	+ 15	- 15	- 9	+ 9
After	5 u	4 u	4.5 u	4.5 u

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

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

In Case 2, when Gabriel gives to Winnie, there is an internal transfer of money from Gabriel 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 Gabriel have
= 5 u + 4 u
= 9 u

Amount that Winnie and Gabriel each has in the end for Case 2
= 9 u ÷ 2
= 4.5 u

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

5 u - 15 = 4.5 u + 9
5 u - 4.5 u = 9 + 15
0.5 u = 24 

1 u = 24 ÷ 0.5 = 48

Amount that Gabriel has
= 5 u - 15
= 5 x 48 - 15
= 240 - 15
= $225 

(b)
Amount that Winnie has
= 4 u + 15
= 4 x 48 + 15
= 192 + 15
= $207

Answer(s): (a) $225; (b) $207