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

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

Number of buttons that Barbara and Nora each had in the end is the same.

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

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

4 p = 20

1 p = 20 ÷ 4 = 5

Number of buttons that Nora had after receiving some buttons from Barbara
= 5 p
= 5 x 5
= 25

Number of buttons that Barbara had after giving to Nora
= 40 - 25
= 15

5 u = 15

1 u = 15 ÷ 5 = 3

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

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

Answer(s): 22