If Xandra gives Paul $23, the amount of money she has will be 25% of his. If Paul gives Xandra $37, he will have the same amount of money as her. How much money did each of them have?
(a) Paul
(b) Xandra

	Case 1		Case 2
	Paul	Xandra	Paul	Xandra
Before	4 u - 23	1 u + 23	2.5 u + 37	2.5 u - 37
Change	+ 23	- 23	- 37	+ 37
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 23 = 2.5 u + 37
4 u - 2.5 u = 37 + 23
1.5 u = 60 

1 u = 60 ÷ 1.5 = 40

Amount that Paul has
= 4 u - 23
= 4 x 40 - 23
= 160 - 23
= $137 

(b)
Amount that Xandra has
= 1 u + 23
= 1 x 40 + 23
= 40 + 23
= $63

Answer(s): (a) $137; (b) $63