If Raeann gives Albert $32, the amount of money she has will be 40% of his. If Albert gives Raeann $37, he will have the same amount of money as her. How much money did each of them have?
(a) Albert
(b) Raeann

	Case 1		Case 2
	Albert	Raeann	Albert	Raeann
Before	5 u - 32	2 u + 32	3.5 u + 37	3.5 u - 37
Change	+ 32	- 32	- 37	+ 37
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

Amount that Raeann 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 - 32 = 3.5 u + 37
5 u - 3.5 u = 37 + 32
1.5 u = 69 

1 u = 69 ÷ 1.5 = 46

Amount that Albert has
= 5 u - 32
= 5 x 46 - 32
= 230 - 32
= $198 

(b)
Amount that Raeann has
= 2 u + 32
= 2 x 46 + 32
= 92 + 32
= $124

Answer(s): (a) $198; (b) $124