If Dana gives Archie $15, the amount of money she has will be 10% of his. If Archie gives Dana $93, he will have the same amount of money as her. How much money did each of them have?
(a) Archie
(b) Dana

	Case 1		Case 2
	Archie	Dana	Archie	Dana
Before	10 u - 15	1 u + 15	5.5 u + 93	5.5 u - 93
Change	+ 15	- 15	- 93	+ 93
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Dana 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 - 15 = 5.5 u + 93
10 u - 5.5 u = 93 + 15
4.5 u = 108 

1 u = 108 ÷ 4.5 = 24

Amount that Archie has
= 10 u - 15
= 10 x 24 - 15
= 240 - 15
= $225 

(b)
Amount that Dana has
= 1 u + 15
= 1 x 24 + 15
= 24 + 15
= $39

Answer(s): (a) $225; (b) $39