If Julie gives Valen $26, the amount of money she has will be 30% of his. If Valen gives Julie $93, he will have the same amount of money as her. How much money did each of them have?
(a) Valen
(b) Julie

	Case 1		Case 2
	Valen	Julie	Valen	Julie
Before	10 u - 26	3 u + 26	6.5 u + 93	6.5 u - 93
Change	+ 26	- 26	- 93	+ 93
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Julie 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 - 26 = 6.5 u + 93
10 u - 6.5 u = 93 + 26
3.5 u = 119 

1 u = 119 ÷ 3.5 = 34

Amount that Valen has
= 10 u - 26
= 10 x 34 - 26
= 340 - 26
= $314 

(b)
Amount that Julie has
= 3 u + 26
= 3 x 34 + 26
= 102 + 26
= $128

Answer(s): (a) $314; (b) $128