If Olivia gives Flynn $19, the amount of money she has will be 10% of his. If Flynn gives Olivia $71, he will have the same amount of money as her. How much money did each of them have?
(a) Flynn
(b) Olivia

	Case 1		Case 2
	Flynn	Olivia	Flynn	Olivia
Before	10 u - 19	1 u + 19	5.5 u + 71	5.5 u - 71
Change	+ 19	- 19	- 71	+ 71
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Olivia 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 - 19 = 5.5 u + 71
10 u - 5.5 u = 71 + 19
4.5 u = 90 

1 u = 90 ÷ 4.5 = 20

Amount that Flynn has
= 10 u - 19
= 10 x 20 - 19
= 200 - 19
= $181 

(b)
Amount that Olivia has
= 1 u + 19
= 1 x 20 + 19
= 20 + 19
= $39

Answer(s): (a) $181; (b) $39