Hilda and Roshel had a total of 48 stickers. Roshel gave ¹₃ of her stickers to Hilda. In return, Hilda gave ¹₅ of the total number of stickers that she had to Roshel. In the end, each girl had the same number of stickers. How many stickers did Hilda have at first?

	Hilda	Roshel	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	30	2 u	48
Before 2	5 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	4 p (24)	24	48

Since Roshel gave some stickers to Hilda and Hilda then gave some stickers to Roshel, it is an internal transfer of stickers between the two girls. So, the total number of stickers remains unchanged.

Number of stickers that Roshel and Hilda each had in the end is the same.

Number of stickers that Hilda had in the end
= 48 ÷ 2
= 24

Number of stickers that Hilda had in the end = 4 p

4 p = 24

1 p = 24 ÷ 4 = 6

Number of stickers that Hilda had after receiving some stickers from Roshel
= 5 p
= 5 x 6
= 30

Number of stickers that Roshel had after giving to Hilda
= 48 - 30
= 18

2 u = 18

1 u = 18 ÷ 2 = 9

Number of stickers that Roshel had at first
= 3 u
= 3 x 9
= 27

Number of stickers that Hilda had at first
= 48 - 27
= 21

Answer(s): 21