Vanessa and Roshel had a total of 24 coins. Roshel gave ¹₄ of her coins to Vanessa. In return, Vanessa gave ¹₃ of the total number of coins that she had to Roshel. In the end, each girl had the same number of coins. How many coins did Vanessa have at first?

	Vanessa	Roshel	Total
Before 1	?	4 u	24
Change 1	+ 1 u	- 1 u
After 1	18	3 u	24
Before 2	3 p	3 u	24
Change 2	- 1 p	+ 1 p
After 2	2 p (12)	12	24

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

Number of coins that Roshel and Vanessa each had in the end is the same.

Number of coins that Vanessa had in the end
= 24 ÷ 2
= 12

Number of coins that Vanessa had in the end = 2 p

2 p = 12

1 p = 12 ÷ 2 = 6

Number of coins that Vanessa had after receiving some coins from Roshel
= 3 p
= 3 x 6
= 18

Number of coins that Roshel had after giving to Vanessa
= 24 - 18
= 6

3 u = 6

1 u = 6 ÷ 3 = 2

Number of coins that Roshel had at first
= 4 u
= 4 x 2
= 8

Number of coins that Vanessa had at first
= 24 - 8
= 16

Answer(s): 16