If Dana gives Jack $26, the amount of money she has will be 25% of his. If Jack gives Dana $34, he will have the same amount of money as her. How much money did each of them have?
(a) Jack
(b) Dana

	Case 1		Case 2
	Jack	Dana	Jack	Dana
Before	4 u - 26	1 u + 26	2.5 u + 34	2.5 u - 34
Change	+ 26	- 26	- 34	+ 34
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Jack gives to Dana, there is an internal transfer of money from Jack to Dana. 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 Dana and Jack have
= 4 u + 1 u
= 5 u

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

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

4 u - 26 = 2.5 u + 34
4 u - 2.5 u = 34 + 26
1.5 u = 60 

1 u = 60 ÷ 1.5 = 40

Amount that Jack has
= 4 u - 26
= 4 x 40 - 26
= 160 - 26
= $134 

(b)
Amount that Dana has
= 1 u + 26
= 1 x 40 + 26
= 40 + 26
= $66

Answer(s): (a) $134; (b) $66