If Fiona gives Caden $26, the amount of money she has will be 30% of his. If Caden gives Fiona $107, he will have the same amount of money as her. How much money did each of them have?
(a) Caden
(b) Fiona

	Case 1		Case 2
	Caden	Fiona	Caden	Fiona
Before	10 u - 26	3 u + 26	6.5 u + 107	6.5 u - 107
Change	+ 26	- 26	- 107	+ 107
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 26 = 6.5 u + 107
10 u - 6.5 u = 107 + 26
3.5 u = 133 

1 u = 133 ÷ 3.5 = 38

Amount that Caden has
= 10 u - 26
= 10 x 38 - 26
= 380 - 26
= $354 

(b)
Amount that Fiona has
= 3 u + 26
= 3 x 38 + 26
= 114 + 26
= $140

Answer(s): (a) $354; (b) $140