If Olivia gives Dylan $39, the amount of money she has will be 25% of his. If Dylan gives Olivia $15, he will have the same amount of money as her. How much money did each of them have?
(a) Dylan
(b) Olivia

	Case 1		Case 2
	Dylan	Olivia	Dylan	Olivia
Before	4 u - 39	1 u + 39	2.5 u + 15	2.5 u - 15
Change	+ 39	- 39	- 15	+ 15
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Dylan gives to Olivia, there is an internal transfer of money from Dylan to Olivia. 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 Olivia and Dylan have
= 4 u + 1 u
= 5 u

Amount that Olivia and Dylan each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 39 = 2.5 u + 15
4 u - 2.5 u = 15 + 39
1.5 u = 54 

1 u = 54 ÷ 1.5 = 36

Amount that Dylan has
= 4 u - 39
= 4 x 36 - 39
= 144 - 39
= $105 

(b)
Amount that Olivia has
= 1 u + 39
= 1 x 36 + 39
= 36 + 39
= $75

Answer(s): (a) $105; (b) $75