If Zoe gives Zeph $17, the amount of money she has will be 30% of his. If Zeph gives Zoe $130, he will have the same amount of money as her. How much money did each of them have?
(a) Zeph
(b) Zoe

	Case 1		Case 2
	Zeph	Zoe	Zeph	Zoe
Before	10 u - 17	3 u + 17	6.5 u + 130	6.5 u - 130
Change	+ 17	- 17	- 130	+ 130
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Zoe 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 - 17 = 6.5 u + 130
10 u - 6.5 u = 130 + 17
3.5 u = 147 

1 u = 147 ÷ 3.5 = 42

Amount that Zeph has
= 10 u - 17
= 10 x 42 - 17
= 420 - 17
= $403 

(b)
Amount that Zoe has
= 3 u + 17
= 3 x 42 + 17
= 126 + 17
= $143

Answer(s): (a) $403; (b) $143