Irene and Barbara had a total of 112 stickers. Barbara gave ¹₅ of her stickers to Irene. In return, Irene gave ¹₈ of the total number of stickers that she had to Barbara. In the end, each girl had the same number of stickers. How many stickers did Irene have at first?

	Irene	Barbara	Total
Before 1	?	5 u	112
Change 1	+ 1 u	- 1 u
After 1	64	4 u	112
Before 2	8 p	4 u	112
Change 2	- 1 p	+ 1 p
After 2	7 p (56)	56	112

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

Number of stickers that Barbara and Irene each had in the end is the same.

Number of stickers that Irene had in the end
= 112 ÷ 2
= 56

Number of stickers that Irene had in the end = 7 p

7 p = 56

1 p = 56 ÷ 7 = 8

Number of stickers that Irene had after receiving some stickers from Barbara
= 8 p
= 8 x 8
= 64

Number of stickers that Barbara had after giving to Irene
= 112 - 64
= 48

4 u = 48

1 u = 48 ÷ 4 = 12

Number of stickers that Barbara had at first
= 5 u
= 5 x 12
= 60

Number of stickers that Irene had at first
= 112 - 60
= 52

Answer(s): 52