If Emily gives David $40, the amount of money she has will be 40% of his. If David gives Emily $2, he will have the same amount of money as her. How much money did each of them have?
(a) David
(b) Emily

	Case 1		Case 2
	David	Emily	David	Emily
Before	5 u - 40	2 u + 40	3.5 u + 2	3.5 u - 2
Change	+ 40	- 40	- 2	+ 2
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 40 = 3.5 u + 2
5 u - 3.5 u = 2 + 40
1.5 u = 42 

1 u = 42 ÷ 1.5 = 28

Amount that David has
= 5 u - 40
= 5 x 28 - 40
= 140 - 40
= $100 

(b)
Amount that Emily has
= 2 u + 40
= 2 x 28 + 40
= 56 + 40
= $96

Answer(s): (a) $100; (b) $96