Kimberly and Tammy had a total of 126 buttons. Tammy gave ¹₄ of her buttons to Kimberly. In return, Kimberly gave ¹₈ of the total number of buttons that she had to Tammy. In the end, each girl had the same number of buttons. How many buttons did Kimberly have at first?

	Kimberly	Tammy	Total
Before 1	?	4 u	126
Change 1	+ 1 u	- 1 u
After 1	72	3 u	126
Before 2	8 p	3 u	126
Change 2	- 1 p	+ 1 p
After 2	7 p (63)	63	126

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

Number of buttons that Tammy and Kimberly each had in the end is the same.

Number of buttons that Kimberly had in the end
= 126 ÷ 2
= 63

Number of buttons that Kimberly had in the end = 7 p

7 p = 63

1 p = 63 ÷ 7 = 9

Number of buttons that Kimberly had after receiving some buttons from Tammy
= 8 p
= 8 x 9
= 72

Number of buttons that Tammy had after giving to Kimberly
= 126 - 72
= 54

3 u = 54

1 u = 54 ÷ 3 = 18

Number of buttons that Tammy had at first
= 4 u
= 4 x 18
= 72

Number of buttons that Kimberly had at first
= 126 - 72
= 54

Answer(s): 54