Victoria and Cindy had a total of 144 beads. Cindy gave ¹₃ of her beads to Victoria. In return, Victoria gave ¹₇ of the total number of beads that she had to Cindy. In the end, each girl had the same number of beads. How many beads did Victoria have at first?

	Victoria	Cindy	Total
Before 1	?	3 u	144
Change 1	+ 1 u	- 1 u
After 1	84	2 u	144
Before 2	7 p	2 u	144
Change 2	- 1 p	+ 1 p
After 2	6 p (72)	72	144

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

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

Number of beads that Victoria had in the end
= 144 ÷ 2
= 72

Number of beads that Victoria had in the end = 6 p

6 p = 72

1 p = 72 ÷ 6 = 12

Number of beads that Victoria had after receiving some beads from Cindy
= 7 p
= 7 x 12
= 84

Number of beads that Cindy had after giving to Victoria
= 144 - 84
= 60

2 u = 60

1 u = 60 ÷ 2 = 30

Number of beads that Cindy had at first
= 3 u
= 3 x 30
= 90

Number of beads that Victoria had at first
= 144 - 90
= 54

Answer(s): 54