Yen and Penelope had a total of 70 coins. Penelope gave ¹₃ of her coins to Yen. In return, Yen gave ¹₈ of the total number of coins that she had to Penelope. In the end, each girl had the same number of coins. How many coins did Yen have at first?

	Yen	Penelope	Total
Before 1	?	3 u	70
Change 1	+ 1 u	- 1 u
After 1	40	2 u	70
Before 2	8 p	2 u	70
Change 2	- 1 p	+ 1 p
After 2	7 p (35)	35	70

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

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

Number of coins that Yen had in the end
= 70 ÷ 2
= 35

Number of coins that Yen had in the end = 7 p

7 p = 35

1 p = 35 ÷ 7 = 5

Number of coins that Yen had after receiving some coins from Penelope
= 8 p
= 8 x 5
= 40

Number of coins that Penelope had after giving to Yen
= 70 - 40
= 30

2 u = 30

1 u = 30 ÷ 2 = 15

Number of coins that Penelope had at first
= 3 u
= 3 x 15
= 45

Number of coins that Yen had at first
= 70 - 45
= 25

Answer(s): 25