If Zoe gives Japheth $35, the amount of money she has will be 10% of his. If Japheth gives Zoe $82, he will have the same amount of money as her. How much money did each of them have?
(a) Japheth
(b) Zoe

	Case 1		Case 2
	Japheth	Zoe	Japheth	Zoe
Before	10 u - 35	1 u + 35	5.5 u + 82	5.5 u - 82
Change	+ 35	- 35	- 82	+ 82
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Japheth gives to Zoe, there is an internal transfer of money from Japheth 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 Japheth have
= 10 u + 1 u
= 11 u

Amount that Zoe and Japheth each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 35 = 5.5 u + 82
10 u - 5.5 u = 82 + 35
4.5 u = 117 

1 u = 117 ÷ 4.5 = 26

Amount that Japheth has
= 10 u - 35
= 10 x 26 - 35
= 260 - 35
= $225 

(b)
Amount that Zoe has
= 1 u + 35
= 1 x 26 + 35
= 26 + 35
= $61

Answer(s): (a) $225; (b) $61