If Fanny gives Ken $31, the amount of money she has will be 30% of his. If Ken gives Fanny $39, he will have the same amount of money as her. How much money did each of them have?
(a) Ken
(b) Fanny

	Case 1		Case 2
	Ken	Fanny	Ken	Fanny
Before	10 u - 31	3 u + 31	6.5 u + 39	6.5 u - 39
Change	+ 31	- 31	- 39	+ 39
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 31 = 6.5 u + 39
10 u - 6.5 u = 39 + 31
3.5 u = 70 

1 u = 70 ÷ 3.5 = 20

Amount that Ken has
= 10 u - 31
= 10 x 20 - 31
= 200 - 31
= $169 

(b)
Amount that Fanny has
= 3 u + 31
= 3 x 20 + 31
= 60 + 31
= $91

Answer(s): (a) $169; (b) $91