If Natalie gives Albert $34, the amount of money she has will be 40% of his. If Albert gives Natalie $26, he will have the same amount of money as her. How much money did each of them have?
(a) Albert
(b) Natalie

	Case 1		Case 2
	Albert	Natalie	Albert	Natalie
Before	5 u - 34	2 u + 34	3.5 u + 26	3.5 u - 26
Change	+ 34	- 34	- 26	+ 26
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Albert gives to Natalie, there is an internal transfer of money from Albert to Natalie. 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 Natalie and Albert have
= 5 u + 2 u
= 7 u

Amount that Natalie and Albert each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

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

5 u - 34 = 3.5 u + 26
5 u - 3.5 u = 26 + 34
1.5 u = 60 

1 u = 60 ÷ 1.5 = 40

Amount that Albert has
= 5 u - 34
= 5 x 40 - 34
= 200 - 34
= $166 

(b)
Amount that Natalie has
= 2 u + 34
= 2 x 40 + 34
= 80 + 34
= $114

Answer(s): (a) $166; (b) $114