If Xylia gives Flynn $29, the amount of money she has will be 30% of his. If Flynn gives Xylia $69, he will have the same amount of money as her. How much money did each of them have?
(a) Flynn
(b) Xylia

	Case 1		Case 2
	Flynn	Xylia	Flynn	Xylia
Before	10 u - 29	3 u + 29	6.5 u + 69	6.5 u - 69
Change	+ 29	- 29	- 69	+ 69
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 29 = 6.5 u + 69
10 u - 6.5 u = 69 + 29
3.5 u = 98 

1 u = 98 ÷ 3.5 = 28

Amount that Flynn has
= 10 u - 29
= 10 x 28 - 29
= 280 - 29
= $251 

(b)
Amount that Xylia has
= 3 u + 29
= 3 x 28 + 29
= 84 + 29
= $113

Answer(s): (a) $251; (b) $113