If Anna gives Sean $31, the amount of money she has will be 25% of his. If Sean gives Anna $26, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Anna

	Case 1		Case 2
	Sean	Anna	Sean	Anna
Before	4 u - 31	1 u + 31	2.5 u + 26	2.5 u - 26
Change	+ 31	- 31	- 26	+ 26
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Sean gives to Anna, there is an internal transfer of money from Sean 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 Sean have
= 4 u + 1 u
= 5 u

Amount that Anna and Sean each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 31 = 2.5 u + 26
4 u - 2.5 u = 26 + 31
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Sean has
= 4 u - 31
= 4 x 38 - 31
= 152 - 31
= $121 

(b)
Amount that Anna has
= 1 u + 31
= 1 x 38 + 31
= 38 + 31
= $69

Answer(s): (a) $121; (b) $69