If Victoria gives Julian $22, the amount of money she has will be 40% of his. If Julian gives Victoria $8, he will have the same amount of money as her. How much money did each of them have?
(a) Julian
(b) Victoria

	Case 1		Case 2
	Julian	Victoria	Julian	Victoria
Before	5 u - 22	2 u + 22	3.5 u + 8	3.5 u - 8
Change	+ 22	- 22	- 8	+ 8
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Julian gives to Victoria, there is an internal transfer of money from Julian to Victoria. 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 Victoria and Julian have
= 5 u + 2 u
= 7 u

Amount that Victoria and Julian each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

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

5 u - 22 = 3.5 u + 8
5 u - 3.5 u = 8 + 22
1.5 u = 30 

1 u = 30 ÷ 1.5 = 20

Amount that Julian has
= 5 u - 22
= 5 x 20 - 22
= 100 - 22
= $78 

(b)
Amount that Victoria has
= 2 u + 22
= 2 x 20 + 22
= 40 + 22
= $62

Answer(s): (a) $78; (b) $62