If Kylie gives Seth $36, the amount of money she has will be 10% of his. If Seth gives Kylie $90, he will have the same amount of money as her. How much money did each of them have?
(a) Seth
(b) Kylie

	Case 1		Case 2
	Seth	Kylie	Seth	Kylie
Before	10 u - 36	1 u + 36	5.5 u + 90	5.5 u - 90
Change	+ 36	- 36	- 90	+ 90
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Seth gives to Kylie, there is an internal transfer of money from Seth 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 Seth have
= 10 u + 1 u
= 11 u

Amount that Kylie and Seth each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 36 = 5.5 u + 90
10 u - 5.5 u = 90 + 36
4.5 u = 126 

1 u = 126 ÷ 4.5 = 28

Amount that Seth has
= 10 u - 36
= 10 x 28 - 36
= 280 - 36
= $244 

(b)
Amount that Kylie has
= 1 u + 36
= 1 x 28 + 36
= 28 + 36
= $64

Answer(s): (a) $244; (b) $64