If Fiona gives Tom $27, the amount of money she has will be 30% of his. If Tom gives Fiona $134, he will have the same amount of money as her. How much money did each of them have?
(a) Tom
(b) Fiona

	Case 1		Case 2
	Tom	Fiona	Tom	Fiona
Before	10 u - 27	3 u + 27	6.5 u + 134	6.5 u - 134
Change	+ 27	- 27	- 134	+ 134
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Tom gives to Fiona, there is an internal transfer of money from Tom to Fiona. 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 Fiona and Tom have
= 10 u + 3 u
= 13 u

Amount that Fiona and Tom each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 27 = 6.5 u + 134
10 u - 6.5 u = 134 + 27
3.5 u = 161 

1 u = 161 ÷ 3.5 = 46

Amount that Tom has
= 10 u - 27
= 10 x 46 - 27
= 460 - 27
= $433 

(b)
Amount that Fiona has
= 3 u + 27
= 3 x 46 + 27
= 138 + 27
= $165

Answer(s): (a) $433; (b) $165