If Kathy gives Caden $30, the amount of money she has will be 25% of his. If Caden gives Kathy $15, he will have the same amount of money as her. How much money did each of them have?
(a) Caden
(b) Kathy

	Case 1		Case 2
	Caden	Kathy	Caden	Kathy
Before	4 u - 30	1 u + 30	2.5 u + 15	2.5 u - 15
Change	+ 30	- 30	- 15	+ 15
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 30 = 2.5 u + 15
4 u - 2.5 u = 15 + 30
1.5 u = 45 

1 u = 45 ÷ 1.5 = 30

Amount that Caden has
= 4 u - 30
= 4 x 30 - 30
= 120 - 30
= $90 

(b)
Amount that Kathy has
= 1 u + 30
= 1 x 30 + 30
= 30 + 30
= $60

Answer(s): (a) $90; (b) $60