If Jane gives Archie $24, the amount of money she has will be 30% of his. If Archie gives Jane $60, he will have the same amount of money as her. How much money did each of them have?
(a) Archie
(b) Jane

	Case 1		Case 2
	Archie	Jane	Archie	Jane
Before	10 u - 24	3 u + 24	6.5 u + 60	6.5 u - 60
Change	+ 24	- 24	- 60	+ 60
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Jane 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 - 24 = 6.5 u + 60
10 u - 6.5 u = 60 + 24
3.5 u = 84 

1 u = 84 ÷ 3.5 = 24

Amount that Archie has
= 10 u - 24
= 10 x 24 - 24
= 240 - 24
= $216 

(b)
Amount that Jane has
= 3 u + 24
= 3 x 24 + 24
= 72 + 24
= $96

Answer(s): (a) $216; (b) $96