If Roshel gives Billy $15, the amount of money she has will be 10% of his. If Billy gives Roshel $183, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Roshel

	Case 1		Case 2
	Billy	Roshel	Billy	Roshel
Before	10 u - 15	1 u + 15	5.5 u + 183	5.5 u - 183
Change	+ 15	- 15	- 183	+ 183
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 15 = 5.5 u + 183
10 u - 5.5 u = 183 + 15
4.5 u = 198 

1 u = 198 ÷ 4.5 = 44

Amount that Billy has
= 10 u - 15
= 10 x 44 - 15
= 440 - 15
= $425 

(b)
Amount that Roshel has
= 1 u + 15
= 1 x 44 + 15
= 44 + 15
= $59

Answer(s): (a) $425; (b) $59