If Tiffany gives Tom $22, the amount of money she has will be 10% of his. If Tom gives Tiffany $104, he will have the same amount of money as her. How much money did each of them have?
(a) Tom
(b) Tiffany

	Case 1		Case 2
	Tom	Tiffany	Tom	Tiffany
Before	10 u - 22	1 u + 22	5.5 u + 104	5.5 u - 104
Change	+ 22	- 22	- 104	+ 104
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 22 = 5.5 u + 104
10 u - 5.5 u = 104 + 22
4.5 u = 126 

1 u = 126 ÷ 4.5 = 28

Amount that Tom has
= 10 u - 22
= 10 x 28 - 22
= 280 - 22
= $258 

(b)
Amount that Tiffany has
= 1 u + 22
= 1 x 28 + 22
= 28 + 22
= $50

Answer(s): (a) $258; (b) $50