If Kimberly gives Sean $39, the amount of money she has will be 30% of his. If Sean gives Kimberly $31, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Kimberly

	Case 1		Case 2
	Sean	Kimberly	Sean	Kimberly
Before	10 u - 39	3 u + 39	6.5 u + 31	6.5 u - 31
Change	+ 39	- 39	- 31	+ 31
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Sean gives to Kimberly, there is an internal transfer of money from Sean 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 Sean have
= 10 u + 3 u
= 13 u

Amount that Kimberly and Sean each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 39 = 6.5 u + 31
10 u - 6.5 u = 31 + 39
3.5 u = 70 

1 u = 70 ÷ 3.5 = 20

Amount that Sean has
= 10 u - 39
= 10 x 20 - 39
= 200 - 39
= $161 

(b)
Amount that Kimberly has
= 3 u + 39
= 3 x 20 + 39
= 60 + 39
= $99

Answer(s): (a) $161; (b) $99