If Gwen gives Archie $30, the amount of money she has will be 10% of his. If Archie gives Gwen $141, he will have the same amount of money as her. How much money did each of them have?
(a) Archie
(b) Gwen

	Case 1		Case 2
	Archie	Gwen	Archie	Gwen
Before	10 u - 30	1 u + 30	5.5 u + 141	5.5 u - 141
Change	+ 30	- 30	- 141	+ 141
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Archie gives to Gwen, there is an internal transfer of money from Archie to Gwen. 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 Gwen and Archie have
= 10 u + 1 u
= 11 u

Amount that Gwen and Archie each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 30 = 5.5 u + 141
10 u - 5.5 u = 141 + 30
4.5 u = 171 

1 u = 171 ÷ 4.5 = 38

Amount that Archie has
= 10 u - 30
= 10 x 38 - 30
= 380 - 30
= $350 

(b)
Amount that Gwen has
= 1 u + 30
= 1 x 38 + 30
= 38 + 30
= $68

Answer(s): (a) $350; (b) $68