Xuan and Betty had a total of 36 marbles. Betty gave ¹₄ of her marbles to Xuan. In return, Xuan gave ¹₇ of the total number of marbles that she had to Betty. In the end, each girl had the same number of marbles. How many marbles did Xuan have at first?

	Xuan	Betty	Total
Before 1	?	4 u	36
Change 1	+ 1 u	- 1 u
After 1	21	3 u	36
Before 2	7 p	3 u	36
Change 2	- 1 p	+ 1 p
After 2	6 p (18)	18	36

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

Number of marbles that Betty and Xuan each had in the end is the same.

Number of marbles that Xuan had in the end
= 36 ÷ 2
= 18

Number of marbles that Xuan had in the end = 6 p

6 p = 18

1 p = 18 ÷ 6 = 3

Number of marbles that Xuan had after receiving some marbles from Betty
= 7 p
= 7 x 3
= 21

Number of marbles that Betty had after giving to Xuan
= 36 - 21
= 15

3 u = 15

1 u = 15 ÷ 3 = 5

Number of marbles that Betty had at first
= 4 u
= 4 x 5
= 20

Number of marbles that Xuan had at first
= 36 - 20
= 16

Answer(s): 16