If Ivory gives Flynn $34, the amount of money she has will be 10% of his. If Flynn gives Ivory $164, he will have the same amount of money as her. How much money did each of them have?
(a) Flynn
(b) Ivory

	Case 1		Case 2
	Flynn	Ivory	Flynn	Ivory
Before	10 u - 34	1 u + 34	5.5 u + 164	5.5 u - 164
Change	+ 34	- 34	- 164	+ 164
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Flynn gives to Ivory, there is an internal transfer of money from Flynn to Ivory. 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 Ivory and Flynn have
= 10 u + 1 u
= 11 u

Amount that Ivory and Flynn each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 34 = 5.5 u + 164
10 u - 5.5 u = 164 + 34
4.5 u = 198 

1 u = 198 ÷ 4.5 = 44

Amount that Flynn has
= 10 u - 34
= 10 x 44 - 34
= 440 - 34
= $406 

(b)
Amount that Ivory has
= 1 u + 34
= 1 x 44 + 34
= 44 + 34
= $78

Answer(s): (a) $406; (b) $78