If Usha gives Charlie $31, the amount of money she has will be 10% of his. If Charlie gives Usha $86, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Usha

	Case 1		Case 2
	Charlie	Usha	Charlie	Usha
Before	10 u - 31	1 u + 31	5.5 u + 86	5.5 u - 86
Change	+ 31	- 31	- 86	+ 86
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Usha 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 - 31 = 5.5 u + 86
10 u - 5.5 u = 86 + 31
4.5 u = 117 

1 u = 117 ÷ 4.5 = 26

Amount that Charlie has
= 10 u - 31
= 10 x 26 - 31
= 260 - 31
= $229 

(b)
Amount that Usha has
= 1 u + 31
= 1 x 26 + 31
= 26 + 31
= $57

Answer(s): (a) $229; (b) $57