If Natalie gives Dylan $35, the amount of money she has will be 10% of his. If Dylan gives Natalie $100, he will have the same amount of money as her. How much money did each of them have?
(a) Dylan
(b) Natalie

	Case 1		Case 2
	Dylan	Natalie	Dylan	Natalie
Before	10 u - 35	1 u + 35	5.5 u + 100	5.5 u - 100
Change	+ 35	- 35	- 100	+ 100
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Dylan gives to Natalie, there is an internal transfer of money from Dylan to Natalie. 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 Natalie and Dylan have
= 10 u + 1 u
= 11 u

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

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

10 u - 35 = 5.5 u + 100
10 u - 5.5 u = 100 + 35
4.5 u = 135 

1 u = 135 ÷ 4.5 = 30

Amount that Dylan has
= 10 u - 35
= 10 x 30 - 35
= 300 - 35
= $265 

(b)
Amount that Natalie has
= 1 u + 35
= 1 x 30 + 35
= 30 + 35
= $65

Answer(s): (a) $265; (b) $65