Nora and Jen had a total of 154 coins. Jen gave ¹₄ of her coins to Nora. In return, Nora gave ¹₈ of the total number of coins that she had to Jen. In the end, each girl had the same number of coins. How many coins did Nora have at first?

	Nora	Jen	Total
Before 1	?	4 u	154
Change 1	+ 1 u	- 1 u
After 1	88	3 u	154
Before 2	8 p	3 u	154
Change 2	- 1 p	+ 1 p
After 2	7 p (77)	77	154

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

Number of coins that Jen and Nora each had in the end is the same.

Number of coins that Nora had in the end
= 154 ÷ 2
= 77

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

7 p = 77

1 p = 77 ÷ 7 = 11

Number of coins that Nora had after receiving some coins from Jen
= 8 p
= 8 x 11
= 88

Number of coins that Jen had after giving to Nora
= 154 - 88
= 66

3 u = 66

1 u = 66 ÷ 3 = 22

Number of coins that Jen had at first
= 4 u
= 4 x 22
= 88

Number of coins that Nora had at first
= 154 - 88
= 66

Answer(s): 66