If Kimberly gives Brandon $23, the amount of money she has will be 10% of his. If Brandon gives Kimberly $157, he will have the same amount of money as her. How much money did each of them have?
(a) Brandon
(b) Kimberly

	Case 1		Case 2
	Brandon	Kimberly	Brandon	Kimberly
Before	10 u - 23	1 u + 23	5.5 u + 157	5.5 u - 157
Change	+ 23	- 23	- 157	+ 157
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Brandon gives to Kimberly, there is an internal transfer of money from Brandon 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 Brandon have
= 10 u + 1 u
= 11 u

Amount that Kimberly and Brandon each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 23 = 5.5 u + 157
10 u - 5.5 u = 157 + 23
4.5 u = 180 

1 u = 180 ÷ 4.5 = 40

Amount that Brandon has
= 10 u - 23
= 10 x 40 - 23
= 400 - 23
= $377 

(b)
Amount that Kimberly has
= 1 u + 23
= 1 x 40 + 23
= 40 + 23
= $63

Answer(s): (a) $377; (b) $63