Jean and Yen had a total of 120 coins. Yen gave ¹₃ of her coins to Jean. In return, Jean gave ¹₇ of the total number of coins that she had to Yen. In the end, each girl had the same number of coins. How many coins did Jean have at first?

	Jean	Yen	Total
Before 1	?	3 u	120
Change 1	+ 1 u	- 1 u
After 1	70	2 u	120
Before 2	7 p	2 u	120
Change 2	- 1 p	+ 1 p
After 2	6 p (60)	60	120

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

Number of coins that Yen and Jean each had in the end is the same.

Number of coins that Jean had in the end
= 120 ÷ 2
= 60

Number of coins that Jean had in the end = 6 p

6 p = 60

1 p = 60 ÷ 6 = 10

Number of coins that Jean had after receiving some coins from Yen
= 7 p
= 7 x 10
= 70

Number of coins that Yen had after giving to Jean
= 120 - 70
= 50

2 u = 50

1 u = 50 ÷ 2 = 25

Number of coins that Yen had at first
= 3 u
= 3 x 25
= 75

Number of coins that Jean had at first
= 120 - 75
= 45

Answer(s): 45