If Olivia gives Luis $34, the amount of money she has will be 30% of his. If Luis gives Olivia $106, he will have the same amount of money as her. How much money did each of them have?
(a) Luis
(b) Olivia

	Case 1		Case 2
	Luis	Olivia	Luis	Olivia
Before	10 u - 34	3 u + 34	6.5 u + 106	6.5 u - 106
Change	+ 34	- 34	- 106	+ 106
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Olivia 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 - 34 = 6.5 u + 106
10 u - 6.5 u = 106 + 34
3.5 u = 140 

1 u = 140 ÷ 3.5 = 40

Amount that Luis has
= 10 u - 34
= 10 x 40 - 34
= 400 - 34
= $366 

(b)
Amount that Olivia has
= 3 u + 34
= 3 x 40 + 34
= 120 + 34
= $154

Answer(s): (a) $366; (b) $154