Cindy and Abi had a total of 120 beads. Abi gave ¹₃ of her beads to Cindy. In return, Cindy gave ¹₆ of the total number of beads that she had to Abi. In the end, each girl had the same number of beads. How many beads did Cindy have at first?

	Cindy	Abi	Total
Before 1	?	3 u	120
Change 1	+ 1 u	- 1 u
After 1	72	2 u	120
Before 2	6 p	2 u	120
Change 2	- 1 p	+ 1 p
After 2	5 p (60)	60	120

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

Number of beads that Abi and Cindy each had in the end is the same.

Number of beads that Cindy had in the end
= 120 ÷ 2
= 60

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

5 p = 60

1 p = 60 ÷ 5 = 12

Number of beads that Cindy had after receiving some beads from Abi
= 6 p
= 6 x 12
= 72

Number of beads that Abi had after giving to Cindy
= 120 - 72
= 48

2 u = 48

1 u = 48 ÷ 2 = 24

Number of beads that Abi had at first
= 3 u
= 3 x 24
= 72

Number of beads that Cindy had at first
= 120 - 72
= 48

Answer(s): 48