If Rachel gives Valen $34, the amount of money she has will be 30% of his. If Valen gives Rachel $36, he will have the same amount of money as her. How much money did each of them have?
(a) Valen
(b) Rachel

	Case 1		Case 2
	Valen	Rachel	Valen	Rachel
Before	10 u - 34	3 u + 34	6.5 u + 36	6.5 u - 36
Change	+ 34	- 34	- 36	+ 36
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 34 = 6.5 u + 36
10 u - 6.5 u = 36 + 34
3.5 u = 70 

1 u = 70 ÷ 3.5 = 20

Amount that Valen has
= 10 u - 34
= 10 x 20 - 34
= 200 - 34
= $166 

(b)
Amount that Rachel has
= 3 u + 34
= 3 x 20 + 34
= 60 + 34
= $94

Answer(s): (a) $166; (b) $94