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

	Case 1		Case 2
	Albert	Rachel	Albert	Rachel
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 Rachel gives to Albert, there is an internal transfer of money from Rachel to Albert.  The total amount that both have remains the same.

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

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

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

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

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