If Natalie gives Luis $30, the amount of money she has will be 30% of his. If Luis gives Natalie $117, he will have the same amount of money as her. How much money did each of them have?
(a) Luis
(b) Natalie

	Case 1		Case 2
	Luis	Natalie	Luis	Natalie
Before	10 u - 30	3 u + 30	6.5 u + 117	6.5 u - 117
Change	+ 30	- 30	- 117	+ 117
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Luis gives to Natalie, there is an internal transfer of money from Luis to Natalie. 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 Natalie and Luis have
= 10 u + 3 u
= 13 u

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

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

10 u - 30 = 6.5 u + 117
10 u - 6.5 u = 117 + 30
3.5 u = 147 

1 u = 147 ÷ 3.5 = 42

Amount that Luis has
= 10 u - 30
= 10 x 42 - 30
= 420 - 30
= $390 

(b)
Amount that Natalie has
= 3 u + 30
= 3 x 42 + 30
= 126 + 30
= $156

Answer(s): (a) $390; (b) $156