Kimberly and Nicole had a total of 40 buttons. Nicole gave ¹₆ of her buttons to Kimberly. In return, Kimberly gave ¹₅ of the total number of buttons that she had to Nicole. In the end, each girl had the same number of buttons. How many buttons did Kimberly have at first?

	Kimberly	Nicole	Total
Before 1	?	6 u	40
Change 1	+ 1 u	- 1 u
After 1	25	5 u	40
Before 2	5 p	5 u	40
Change 2	- 1 p	+ 1 p
After 2	4 p (20)	20	40

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

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

Number of buttons that Kimberly had in the end
= 40 ÷ 2
= 20

Number of buttons that Kimberly had in the end = 4 p

4 p = 20

1 p = 20 ÷ 4 = 5

Number of buttons that Kimberly had after receiving some buttons from Nicole
= 5 p
= 5 x 5
= 25

Number of buttons that Nicole had after giving to Kimberly
= 40 - 25
= 15

5 u = 15

1 u = 15 ÷ 5 = 3

Number of buttons that Nicole had at first
= 6 u
= 6 x 3
= 18

Number of buttons that Kimberly had at first
= 40 - 18
= 22

Answer(s): 22