If Kylie gives Ethan $17, the amount of money she has will be 25% of his. If Ethan gives Kylie $25, he will have the same amount of money as her. How much money did each of them have?
(a) Ethan
(b) Kylie

	Case 1		Case 2
	Ethan	Kylie	Ethan	Kylie
Before	4 u - 17	1 u + 17	2.5 u + 25	2.5 u - 25
Change	+ 17	- 17	- 25	+ 25
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

Amount that Kylie 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 - 17 = 2.5 u + 25
4 u - 2.5 u = 25 + 17
1.5 u = 42 

1 u = 42 ÷ 1.5 = 28

Amount that Ethan has
= 4 u - 17
= 4 x 28 - 17
= 112 - 17
= $95 

(b)
Amount that Kylie has
= 1 u + 17
= 1 x 28 + 17
= 28 + 17
= $45

Answer(s): (a) $95; (b) $45