If Kimberly gives Carl $29, the amount of money she has will be 40% of his. If Carl gives Kimberly $40, he will have the same amount of money as her. How much money did each of them have?
(a) Carl
(b) Kimberly

	Case 1		Case 2
	Carl	Kimberly	Carl	Kimberly
Before	5 u - 29	2 u + 29	3.5 u + 40	3.5 u - 40
Change	+ 29	- 29	- 40	+ 40
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 29 = 3.5 u + 40
5 u - 3.5 u = 40 + 29
1.5 u = 69 

1 u = 69 ÷ 1.5 = 46

Amount that Carl has
= 5 u - 29
= 5 x 46 - 29
= 230 - 29
= $201 

(b)
Amount that Kimberly has
= 2 u + 29
= 2 x 46 + 29
= 92 + 29
= $121

Answer(s): (a) $201; (b) $121