If Kimberly gives Jack $19, the amount of money she has will be 80% of his. If Jack gives Kimberly $4, he will have the same amount of money as her. How much money did each of them have?
(a) Jack
(b) Kimberly

	Case 1		Case 2
	Jack	Kimberly	Jack	Kimberly
Before	5 u - 19	4 u + 19	4.5 u + 4	4.5 u - 4
Change	+ 19	- 19	- 4	+ 4
After	5 u	4 u	4.5 u	4.5 u

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

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

In Case 2, when Jack gives to Kimberly, there is an internal transfer of money from Jack 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 Jack have
= 5 u + 4 u
= 9 u

Amount that Kimberly and Jack each has in the end for Case 2
= 9 u ÷ 2
= 4.5 u

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

5 u - 19 = 4.5 u + 4
5 u - 4.5 u = 4 + 19
0.5 u = 23 

1 u = 23 ÷ 0.5 = 46

Amount that Jack has
= 5 u - 19
= 5 x 46 - 19
= 230 - 19
= $211 

(b)
Amount that Kimberly has
= 4 u + 19
= 4 x 46 + 19
= 184 + 19
= $203

Answer(s): (a) $211; (b) $203