Sarah and Nora had a total of 70 coins. Nora gave ¹₄ of her coins to Sarah. In return, Sarah gave ¹₈ of the total number of coins that she had to Nora. In the end, each girl had the same number of coins. How many coins did Sarah have at first?

	Sarah	Nora	Total
Before 1	?	4 u	70
Change 1	+ 1 u	- 1 u
After 1	40	3 u	70
Before 2	8 p	3 u	70
Change 2	- 1 p	+ 1 p
After 2	7 p (35)	35	70

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

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

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

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

7 p = 35

1 p = 35 ÷ 7 = 5

Number of coins that Sarah had after receiving some coins from Nora
= 8 p
= 8 x 5
= 40

Number of coins that Nora had after giving to Sarah
= 70 - 40
= 30

3 u = 30

1 u = 30 ÷ 3 = 10

Number of coins that Nora had at first
= 4 u
= 4 x 10
= 40

Number of coins that Sarah had at first
= 70 - 40
= 30

Answer(s): 30