If Xylia gives Charlie $37, the amount of money she has will be 10% of his. If Charlie gives Xylia $62, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Xylia

	Case 1		Case 2
	Charlie	Xylia	Charlie	Xylia
Before	10 u - 37	1 u + 37	5.5 u + 62	5.5 u - 62
Change	+ 37	- 37	- 62	+ 62
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Charlie gives to Xylia, there is an internal transfer of money from Charlie 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 Charlie have
= 10 u + 1 u
= 11 u

Amount that Xylia and Charlie each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 37 = 5.5 u + 62
10 u - 5.5 u = 62 + 37
4.5 u = 99 

1 u = 99 ÷ 4.5 = 22

Amount that Charlie has
= 10 u - 37
= 10 x 22 - 37
= 220 - 37
= $183 

(b)
Amount that Xylia has
= 1 u + 37
= 1 x 22 + 37
= 22 + 37
= $59

Answer(s): (a) $183; (b) $59