Joelle and Kathy have some macarons each. If Joelle gives Kathy 13 macarons, Joelle will have ⁴₉ as many macarons as Kathy. If Joelle gives Kathy 3 macarons, they will have an equal number of macarons. How many macarons does Joelle have at first?

	Case 1		Case 2
	Joelle	Kathy	Joelle	Kathy
Before	4 u + 13	9 u - 13	6.5 u + 3	6.5 u - 3
Change	- 13	+ 13	- 3	+ 3
After	4 u	9 u	6.5 u	6.5 u

Total number of macarons that Joelle and Kathy have
= 4 u + 9 u
= 13 u 

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

Number of macarons that Joelle and Kathy each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u

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

6.5 u + 3 = 4 u + 13
6.5 u - 4 u = 13 - 3
0.5 u = 10

1 u = 10 ÷ 0.5 = 20

Number of macarons that Joelle has
= 4 u + 13
= 4 x 20 + 13
= 80 + 13
= 93

Answer(s): 93