If Anna gives Tim $38, the amount of money she has will be 25% of his. If Tim gives Anna $37, he will have the same amount of money as her. How much money did each of them have?
(a) Tim
(b) Anna

	Case 1		Case 2
	Tim	Anna	Tim	Anna
Before	4 u - 38	1 u + 38	2.5 u + 37	2.5 u - 37
Change	+ 38	- 38	- 37	+ 37
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 38 = 2.5 u + 37
4 u - 2.5 u = 37 + 38
1.5 u = 75 

1 u = 75 ÷ 1.5 = 50

Amount that Tim has
= 4 u - 38
= 4 x 50 - 38
= 200 - 38
= $162 

(b)
Amount that Anna has
= 1 u + 38
= 1 x 50 + 38
= 50 + 38
= $88

Answer(s): (a) $162; (b) $88