Fanny and Kathy have some macarons each. If Fanny gives Kathy 17 macarons, Fanny will have ²₃ as many macarons as Kathy. If Fanny gives Kathy 2 macarons, they will have an equal number of macarons. How many macarons does Kathy have at first?

	Case 1		Case 2
	Fanny	Kathy	Fanny	Kathy
Before	2 u + 17	3 u - 17	2.5 u + 2	2.5 u - 2
Change	- 17	+ 17	- 2	+ 2
After	2 u	3 u	2.5 u	2.5 u

Total number of macarons that Fanny and Kathy have
= 2 u + 3 u
= 5 u 

Number of macarons that Fanny and Kathy each has in the end is the same.

Number of macarons that Fanny and Kathy each has in the end in Case 2
= 5 u ÷ 2
= 2.5 u

Number of macarons that Fanny had at first is the same in Case 1 and Case 2.

2.5 u + 2 = 2 u + 17
2.5 u - 2 u = 17 - 2
0.5 u = 15

1 u = 15 ÷ 0.5 = 30

Number of macarons that Kathy has
= 3 u - 17
= 3 x 30 - 17
= 90 - 17
= 73

Answer(s): 73