If Tina gives Ian $35, the amount of money she has will be 10% of his. If Ian gives Tina $73, he will have the same amount of money as her. How much money did each of them have?
(a) Ian
(b) Tina

	Case 1		Case 2
	Ian	Tina	Ian	Tina
Before	10 u - 35	1 u + 35	5.5 u + 73	5.5 u - 73
Change	+ 35	- 35	- 73	+ 73
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 35 = 5.5 u + 73
10 u - 5.5 u = 73 + 35
4.5 u = 108 

1 u = 108 ÷ 4.5 = 24

Amount that Ian has
= 10 u - 35
= 10 x 24 - 35
= 240 - 35
= $205 

(b)
Amount that Tina has
= 1 u + 35
= 1 x 24 + 35
= 24 + 35
= $59

Answer(s): (a) $205; (b) $59