Pamela and Gabby had a total of 84 buttons. Gabby gave ¹₄ of her buttons to Pamela. In return, Pamela gave ¹₈ of the total number of buttons that she had to Gabby. In the end, each girl had the same number of buttons. How many buttons did Pamela have at first?

	Pamela	Gabby	Total
Before 1	?	4 u	84
Change 1	+ 1 u	- 1 u
After 1	48	3 u	84
Before 2	8 p	3 u	84
Change 2	- 1 p	+ 1 p
After 2	7 p (42)	42	84

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

Number of buttons that Gabby and Pamela each had in the end is the same.

Number of buttons that Pamela had in the end
= 84 ÷ 2
= 42

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

7 p = 42

1 p = 42 ÷ 7 = 6

Number of buttons that Pamela had after receiving some buttons from Gabby
= 8 p
= 8 x 6
= 48

Number of buttons that Gabby had after giving to Pamela
= 84 - 48
= 36

3 u = 36

1 u = 36 ÷ 3 = 12

Number of buttons that Gabby had at first
= 4 u
= 4 x 12
= 48

Number of buttons that Pamela had at first
= 84 - 48
= 36

Answer(s): 36