Xandra and Tiffany had a total of 120 buttons. Tiffany gave ¹₃ of her buttons to Xandra. In return, Xandra gave ¹₇ of the total number of buttons that she had to Tiffany. In the end, each girl had the same number of buttons. How many buttons did Xandra have at first?

	Xandra	Tiffany	Total
Before 1	?	3 u	120
Change 1	+ 1 u	- 1 u
After 1	70	2 u	120
Before 2	7 p	2 u	120
Change 2	- 1 p	+ 1 p
After 2	6 p (60)	60	120

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

Number of buttons that Tiffany and Xandra each had in the end is the same.

Number of buttons that Xandra had in the end
= 120 ÷ 2
= 60

Number of buttons that Xandra had in the end = 6 p

6 p = 60

1 p = 60 ÷ 6 = 10

Number of buttons that Xandra had after receiving some buttons from Tiffany
= 7 p
= 7 x 10
= 70

Number of buttons that Tiffany had after giving to Xandra
= 120 - 70
= 50

2 u = 50

1 u = 50 ÷ 2 = 25

Number of buttons that Tiffany had at first
= 3 u
= 3 x 25
= 75

Number of buttons that Xandra had at first
= 120 - 75
= 45

Answer(s): 45