Yen and Tiffany had a total of 98 marbles. Tiffany gave ¹₃ of her marbles to Yen. In return, Yen gave ¹₈ of the total number of marbles that she had to Tiffany. In the end, each girl had the same number of marbles. How many marbles did Yen have at first?

	Yen	Tiffany	Total
Before 1	?	3 u	98
Change 1	+ 1 u	- 1 u
After 1	56	2 u	98
Before 2	8 p	2 u	98
Change 2	- 1 p	+ 1 p
After 2	7 p (49)	49	98

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

Number of marbles that Tiffany and Yen each had in the end is the same.

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

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

7 p = 49

1 p = 49 ÷ 7 = 7

Number of marbles that Yen had after receiving some marbles from Tiffany
= 8 p
= 8 x 7
= 56

Number of marbles that Tiffany had after giving to Yen
= 98 - 56
= 42

2 u = 42

1 u = 42 ÷ 2 = 21

Number of marbles that Tiffany had at first
= 3 u
= 3 x 21
= 63

Number of marbles that Yen had at first
= 98 - 63
= 35

Answer(s): 35