Yen and Gem had a total of 60 stickers. Gem gave ¹₆ of her stickers to Yen. In return, Yen gave ¹₄ of the total number of stickers that she had to Gem. In the end, each girl had the same number of stickers. How many stickers did Yen have at first?

	Yen	Gem	Total
Before 1	?	6 u	60
Change 1	+ 1 u	- 1 u
After 1	40	5 u	60
Before 2	4 p	5 u	60
Change 2	- 1 p	+ 1 p
After 2	3 p (30)	30	60

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

Number of stickers that Gem and Yen each had in the end is the same.

Number of stickers that Yen had in the end
= 60 ÷ 2
= 30

Number of stickers that Yen had in the end = 3 p

3 p = 30

1 p = 30 ÷ 3 = 10

Number of stickers that Yen had after receiving some stickers from Gem
= 4 p
= 4 x 10
= 40

Number of stickers that Gem had after giving to Yen
= 60 - 40
= 20

5 u = 20

1 u = 20 ÷ 5 = 4

Number of stickers that Gem had at first
= 6 u
= 6 x 4
= 24

Number of stickers that Yen had at first
= 60 - 24
= 36

Answer(s): 36