If Natalie gives David $22, the amount of money she has will be 40% of his. If David gives Natalie $20, he will have the same amount of money as her. How much money did each of them have?
(a) David
(b) Natalie

	Case 1		Case 2
	David	Natalie	David	Natalie
Before	5 u - 22	2 u + 22	3.5 u + 20	3.5 u - 20
Change	+ 22	- 22	- 20	+ 20
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

Amount that Natalie 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 - 22 = 3.5 u + 20
5 u - 3.5 u = 20 + 22
1.5 u = 42 

1 u = 42 ÷ 1.5 = 28

Amount that David has
= 5 u - 22
= 5 x 28 - 22
= 140 - 22
= $118 

(b)
Amount that Natalie has
= 2 u + 22
= 2 x 28 + 22
= 56 + 22
= $78

Answer(s): (a) $118; (b) $78