If Anna gives Riordan $32, the amount of money she has will be 40% of his. If Riordan gives Anna $25, he will have the same amount of money as her. How much money did each of them have?
(a) Riordan
(b) Anna

	Case 1		Case 2
	Riordan	Anna	Riordan	Anna
Before	5 u - 32	2 u + 32	3.5 u + 25	3.5 u - 25
Change	+ 32	- 32	- 25	+ 25
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Riordan gives to Anna, there is an internal transfer of money from Riordan to Anna. 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 Anna and Riordan have
= 5 u + 2 u
= 7 u

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

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

5 u - 32 = 3.5 u + 25
5 u - 3.5 u = 25 + 32
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Riordan has
= 5 u - 32
= 5 x 38 - 32
= 190 - 32
= $158 

(b)
Amount that Anna has
= 2 u + 32
= 2 x 38 + 32
= 76 + 32
= $108

Answer(s): (a) $158; (b) $108