If Marion gives Sam $21, the amount of money she has will be 40% of his. If Sam gives Marion $45, he will have the same amount of money as her. How much money did each of them have?
(a) Sam
(b) Marion

	Case 1		Case 2
	Sam	Marion	Sam	Marion
Before	5 u - 21	2 u + 21	3.5 u + 45	3.5 u - 45
Change	+ 21	- 21	- 45	+ 45
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 21 = 3.5 u + 45
5 u - 3.5 u = 45 + 21
1.5 u = 66 

1 u = 66 ÷ 1.5 = 44

Amount that Sam has
= 5 u - 21
= 5 x 44 - 21
= 220 - 21
= $199 

(b)
Amount that Marion has
= 2 u + 21
= 2 x 44 + 21
= 88 + 21
= $109

Answer(s): (a) $199; (b) $109