If Hazel gives Charlie $22, the amount of money she has will be 10% of his. If Charlie gives Hazel $194, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Hazel

	Case 1		Case 2
	Charlie	Hazel	Charlie	Hazel
Before	10 u - 22	1 u + 22	5.5 u + 194	5.5 u - 194
Change	+ 22	- 22	- 194	+ 194
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Hazel 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 - 22 = 5.5 u + 194
10 u - 5.5 u = 194 + 22
4.5 u = 216 

1 u = 216 ÷ 4.5 = 48

Amount that Charlie has
= 10 u - 22
= 10 x 48 - 22
= 480 - 22
= $458 

(b)
Amount that Hazel has
= 1 u + 22
= 1 x 48 + 22
= 48 + 22
= $70

Answer(s): (a) $458; (b) $70