If Zoe gives Luis $33, the amount of money she has will be 30% of his. If Luis gives Zoe $37, he will have the same amount of money as her. How much money did each of them have?
(a) Luis
(b) Zoe

	Case 1		Case 2
	Luis	Zoe	Luis	Zoe
Before	10 u - 33	3 u + 33	6.5 u + 37	6.5 u - 37
Change	+ 33	- 33	- 37	+ 37
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Zoe 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 - 33 = 6.5 u + 37
10 u - 6.5 u = 37 + 33
3.5 u = 70 

1 u = 70 ÷ 3.5 = 20

Amount that Luis has
= 10 u - 33
= 10 x 20 - 33
= 200 - 33
= $167 

(b)
Amount that Zoe has
= 3 u + 33
= 3 x 20 + 33
= 60 + 33
= $93

Answer(s): (a) $167; (b) $93