If Elyse gives Archie $32, the amount of money she has will be 30% of his. If Archie gives Elyse $115, he will have the same amount of money as her. How much money did each of them have?
(a) Archie
(b) Elyse

	Case 1		Case 2
	Archie	Elyse	Archie	Elyse
Before	10 u - 32	3 u + 32	6.5 u + 115	6.5 u - 115
Change	+ 32	- 32	- 115	+ 115
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Archie gives to Elyse, there is an internal transfer of money from Archie to Elyse. 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 Elyse and Archie have
= 10 u + 3 u
= 13 u

Amount that Elyse and Archie each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 32 = 6.5 u + 115
10 u - 6.5 u = 115 + 32
3.5 u = 147 

1 u = 147 ÷ 3.5 = 42

Amount that Archie has
= 10 u - 32
= 10 x 42 - 32
= 420 - 32
= $388 

(b)
Amount that Elyse has
= 3 u + 32
= 3 x 42 + 32
= 126 + 32
= $158

Answer(s): (a) $388; (b) $158