If Xylia gives George $23, the amount of money she has will be 40% of his. If George gives Xylia $46, he will have the same amount of money as her. How much money did each of them have?
(a) George
(b) Xylia

	Case 1		Case 2
	George	Xylia	George	Xylia
Before	5 u - 23	2 u + 23	3.5 u + 46	3.5 u - 46
Change	+ 23	- 23	- 46	+ 46
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 23 = 3.5 u + 46
5 u - 3.5 u = 46 + 23
1.5 u = 69 

1 u = 69 ÷ 1.5 = 46

Amount that George has
= 5 u - 23
= 5 x 46 - 23
= 230 - 23
= $207 

(b)
Amount that Xylia has
= 2 u + 23
= 2 x 46 + 23
= 92 + 23
= $115

Answer(s): (a) $207; (b) $115