If Sabrina gives Simon $35, the amount of money she has will be 10% of his. If Simon gives Sabrina $127, he will have the same amount of money as her. How much money did each of them have?
(a) Simon
(b) Sabrina

	Case 1		Case 2
	Simon	Sabrina	Simon	Sabrina
Before	10 u - 35	1 u + 35	5.5 u + 127	5.5 u - 127
Change	+ 35	- 35	- 127	+ 127
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 35 = 5.5 u + 127
10 u - 5.5 u = 127 + 35
4.5 u = 162 

1 u = 162 ÷ 4.5 = 36

Amount that Simon has
= 10 u - 35
= 10 x 36 - 35
= 360 - 35
= $325 

(b)
Amount that Sabrina has
= 1 u + 35
= 1 x 36 + 35
= 36 + 35
= $71

Answer(s): (a) $325; (b) $71