Tiffany and Anna had a total of 48 buttons. Anna gave ¹₄ of her buttons to Tiffany. In return, Tiffany gave ¹₃ of the total number of buttons that she had to Anna. In the end, each girl had the same number of buttons. How many buttons did Tiffany have at first?

	Tiffany	Anna	Total
Before 1	?	4 u	48
Change 1	+ 1 u	- 1 u
After 1	36	3 u	48
Before 2	3 p	3 u	48
Change 2	- 1 p	+ 1 p
After 2	2 p (24)	24	48

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

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

Number of buttons that Tiffany had in the end
= 48 ÷ 2
= 24

Number of buttons that Tiffany had in the end = 2 p

2 p = 24

1 p = 24 ÷ 2 = 12

Number of buttons that Tiffany had after receiving some buttons from Anna
= 3 p
= 3 x 12
= 36

Number of buttons that Anna had after giving to Tiffany
= 48 - 36
= 12

3 u = 12

1 u = 12 ÷ 3 = 4

Number of buttons that Anna had at first
= 4 u
= 4 x 4
= 16

Number of buttons that Tiffany had at first
= 48 - 16
= 32

Answer(s): 32