Pamela and Vanessa had a total of 98 marbles. Vanessa gave ¹₄ of her marbles to Pamela. In return, Pamela gave ¹₈ of the total number of marbles that she had to Vanessa. In the end, each girl had the same number of marbles. How many marbles did Pamela have at first?

	Pamela	Vanessa	Total
Before 1	?	4 u	98
Change 1	+ 1 u	- 1 u
After 1	56	3 u	98
Before 2	8 p	3 u	98
Change 2	- 1 p	+ 1 p
After 2	7 p (49)	49	98

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

Number of marbles that Vanessa and Pamela each had in the end is the same.

Number of marbles that Pamela had in the end
= 98 ÷ 2
= 49

Number of marbles that Pamela had in the end = 7 p

7 p = 49

1 p = 49 ÷ 7 = 7

Number of marbles that Pamela had after receiving some marbles from Vanessa
= 8 p
= 8 x 7
= 56

Number of marbles that Vanessa had after giving to Pamela
= 98 - 56
= 42

3 u = 42

1 u = 42 ÷ 3 = 14

Number of marbles that Vanessa had at first
= 4 u
= 4 x 14
= 56

Number of marbles that Pamela had at first
= 98 - 56
= 42

Answer(s): 42