If Fiona gives Daniel $16, the amount of money she has will be 40% of his. If Daniel gives Fiona $29, he will have the same amount of money as her. How much money did each of them have?
(a) Daniel
(b) Fiona

	Case 1		Case 2
	Daniel	Fiona	Daniel	Fiona
Before	5 u - 16	2 u + 16	3.5 u + 29	3.5 u - 29
Change	+ 16	- 16	- 29	+ 29
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Daniel gives to Fiona, there is an internal transfer of money from Daniel 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 Daniel have
= 5 u + 2 u
= 7 u

Amount that Fiona and Daniel each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

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

5 u - 16 = 3.5 u + 29
5 u - 3.5 u = 29 + 16
1.5 u = 45 

1 u = 45 ÷ 1.5 = 30

Amount that Daniel has
= 5 u - 16
= 5 x 30 - 16
= 150 - 16
= $134 

(b)
Amount that Fiona has
= 2 u + 16
= 2 x 30 + 16
= 60 + 16
= $76

Answer(s): (a) $134; (b) $76