If Yen gives Albert $14, the amount of money she has will be 10% of his. If Albert gives Yen $112, he will have the same amount of money as her. How much money did each of them have?
(a) Albert
(b) Yen

	Case 1		Case 2
	Albert	Yen	Albert	Yen
Before	10 u - 14	1 u + 14	5.5 u + 112	5.5 u - 112
Change	+ 14	- 14	- 112	+ 112
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Yen 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 - 14 = 5.5 u + 112
10 u - 5.5 u = 112 + 14
4.5 u = 126 

1 u = 126 ÷ 4.5 = 28

Amount that Albert has
= 10 u - 14
= 10 x 28 - 14
= 280 - 14
= $266 

(b)
Amount that Yen has
= 1 u + 14
= 1 x 28 + 14
= 28 + 14
= $42

Answer(s): (a) $266; (b) $42