Esther and Barbara have some macarons each. If Esther gives Barbara 13 macarons, Esther will have ⁵₈ as many macarons as Barbara. If Esther gives Barbara 5 macarons, they will have an equal number of macarons. How many macarons does Esther have at first?

	Case 1		Case 2
	Esther	Barbara	Esther	Barbara
Before	5 u + 13	8 u - 13	6.5 u + 5	6.5 u - 5
Change	- 13	+ 13	- 5	+ 5
After	5 u	8 u	6.5 u	6.5 u

Total number of macarons that Esther and Barbara have
= 5 u + 8 u
= 13 u 

Number of macarons that Esther and Barbara each has in the end is the same.

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

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

6.5 u + 5 = 5 u + 13
6.5 u - 5 u = 13 - 5
0.5 u = 8

1 u = 8 ÷ 0.5 = 16

Number of macarons that Esther has
= 5 u + 13
= 5 x 16 + 13
= 80 + 13
= 93

Answer(s): 93