If Anna gives Zeph $39, the amount of money she has will be 30% of his. If Zeph gives Anna $108, he will have the same amount of money as her. How much money did each of them have?
(a) Zeph
(b) Anna

	Case 1		Case 2
	Zeph	Anna	Zeph	Anna
Before	10 u - 39	3 u + 39	6.5 u + 108	6.5 u - 108
Change	+ 39	- 39	- 108	+ 108
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 39 = 6.5 u + 108
10 u - 6.5 u = 108 + 39
3.5 u = 147 

1 u = 147 ÷ 3.5 = 42

Amount that Zeph has
= 10 u - 39
= 10 x 42 - 39
= 420 - 39
= $381 

(b)
Amount that Anna has
= 3 u + 39
= 3 x 42 + 39
= 126 + 39
= $165

Answer(s): (a) $381; (b) $165