If Jaslyn gives Valen $26, the amount of money she has will be 10% of his. If Valen gives Jaslyn $100, he will have the same amount of money as her. How much money did each of them have?
(a) Valen
(b) Jaslyn

	Case 1		Case 2
	Valen	Jaslyn	Valen	Jaslyn
Before	10 u - 26	1 u + 26	5.5 u + 100	5.5 u - 100
Change	+ 26	- 26	- 100	+ 100
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Valen gives to Jaslyn, there is an internal transfer of money from Valen to Jaslyn. 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 Jaslyn and Valen have
= 10 u + 1 u
= 11 u

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

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

10 u - 26 = 5.5 u + 100
10 u - 5.5 u = 100 + 26
4.5 u = 126 

1 u = 126 ÷ 4.5 = 28

Amount that Valen has
= 10 u - 26
= 10 x 28 - 26
= 280 - 26
= $254 

(b)
Amount that Jaslyn has
= 1 u + 26
= 1 x 28 + 26
= 28 + 26
= $54

Answer(s): (a) $254; (b) $54