Cindy and Yen had a total of 20 buttons. Yen gave ¹₃ of her buttons to Cindy. In return, Cindy gave ¹₆ of the total number of buttons that she had to Yen. In the end, each girl had the same number of buttons. How many buttons did Cindy have at first?

	Cindy	Yen	Total
Before 1	?	3 u	20
Change 1	+ 1 u	- 1 u
After 1	12	2 u	20
Before 2	6 p	2 u	20
Change 2	- 1 p	+ 1 p
After 2	5 p (10)	10	20

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

Number of buttons that Yen and Cindy each had in the end is the same.

Number of buttons that Cindy had in the end
= 20 ÷ 2
= 10

Number of buttons that Cindy had in the end = 5 p

5 p = 10

1 p = 10 ÷ 5 = 2

Number of buttons that Cindy had after receiving some buttons from Yen
= 6 p
= 6 x 2
= 12

Number of buttons that Yen had after giving to Cindy
= 20 - 12
= 8

2 u = 8

1 u = 8 ÷ 2 = 4

Number of buttons that Yen had at first
= 3 u
= 3 x 4
= 12

Number of buttons that Cindy had at first
= 20 - 12
= 8

Answer(s): 8