If Barbara gives Fabian $29, the amount of money she has will be 30% of his. If Fabian gives Barbara $118, he will have the same amount of money as her. How much money did each of them have?
(a) Fabian
(b) Barbara

	Case 1		Case 2
	Fabian	Barbara	Fabian	Barbara
Before	10 u - 29	3 u + 29	6.5 u + 118	6.5 u - 118
Change	+ 29	- 29	- 118	+ 118
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 29 = 6.5 u + 118
10 u - 6.5 u = 118 + 29
3.5 u = 147 

1 u = 147 ÷ 3.5 = 42

Amount that Fabian has
= 10 u - 29
= 10 x 42 - 29
= 420 - 29
= $391 

(b)
Amount that Barbara has
= 3 u + 29
= 3 x 42 + 29
= 126 + 29
= $155

Answer(s): (a) $391; (b) $155