If Rachel gives Ethan $24, the amount of money she has will be 25% of his. If Ethan gives Rachel $12, he will have the same amount of money as her. How much money did each of them have?
(a) Ethan
(b) Rachel

	Case 1		Case 2
	Ethan	Rachel	Ethan	Rachel
Before	4 u - 24	1 u + 24	2.5 u + 12	2.5 u - 12
Change	+ 24	- 24	- 12	+ 12
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Ethan gives to Rachel, there is an internal transfer of money from Ethan 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 Ethan have
= 4 u + 1 u
= 5 u

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

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

4 u - 24 = 2.5 u + 12
4 u - 2.5 u = 12 + 24
1.5 u = 36 

1 u = 36 ÷ 1.5 = 24

Amount that Ethan has
= 4 u - 24
= 4 x 24 - 24
= 96 - 24
= $72 

(b)
Amount that Rachel has
= 1 u + 24
= 1 x 24 + 24
= 24 + 24
= $48

Answer(s): (a) $72; (b) $48