If Lucy gives Brandon $16, the amount of money she has will be 10% of his. If Brandon gives Lucy $200, he will have the same amount of money as her. How much money did each of them have?
(a) Brandon
(b) Lucy

	Case 1		Case 2
	Brandon	Lucy	Brandon	Lucy
Before	10 u - 16	1 u + 16	5.5 u + 200	5.5 u - 200
Change	+ 16	- 16	- 200	+ 200
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Lucy 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 - 16 = 5.5 u + 200
10 u - 5.5 u = 200 + 16
4.5 u = 216 

1 u = 216 ÷ 4.5 = 48

Amount that Brandon has
= 10 u - 16
= 10 x 48 - 16
= 480 - 16
= $464 

(b)
Amount that Lucy has
= 1 u + 16
= 1 x 48 + 16
= 48 + 16
= $64

Answer(s): (a) $464; (b) $64