If Kylie gives Asher $15, the amount of money she has will be 25% of his. If Asher gives Kylie $36, he will have the same amount of money as her. How much money did each of them have?
(a) Asher
(b) Kylie

	Case 1		Case 2
	Asher	Kylie	Asher	Kylie
Before	4 u - 15	1 u + 15	2.5 u + 36	2.5 u - 36
Change	+ 15	- 15	- 36	+ 36
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 15 = 2.5 u + 36
4 u - 2.5 u = 36 + 15
1.5 u = 51 

1 u = 51 ÷ 1.5 = 34

Amount that Asher has
= 4 u - 15
= 4 x 34 - 15
= 136 - 15
= $121 

(b)
Amount that Kylie has
= 1 u + 15
= 1 x 34 + 15
= 34 + 15
= $49

Answer(s): (a) $121; (b) $49