If Min gives Archie $28, the amount of money she has will be 10% of his. If Archie gives Min $125, he will have the same amount of money as her. How much money did each of them have?
(a) Archie
(b) Min

	Case 1		Case 2
	Archie	Min	Archie	Min
Before	10 u - 28	1 u + 28	5.5 u + 125	5.5 u - 125
Change	+ 28	- 28	- 125	+ 125
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Min 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 - 28 = 5.5 u + 125
10 u - 5.5 u = 125 + 28
4.5 u = 153 

1 u = 153 ÷ 4.5 = 34

Amount that Archie has
= 10 u - 28
= 10 x 34 - 28
= 340 - 28
= $312 

(b)
Amount that Min has
= 1 u + 28
= 1 x 34 + 28
= 34 + 28
= $62

Answer(s): (a) $312; (b) $62