Sabrina and Cindy had a total of 72 beads. Cindy gave ¹₄ of her beads to Sabrina. In return, Sabrina 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 Sabrina have at first?

	Sabrina	Cindy	Total
Before 1	?	4 u	72
Change 1	+ 1 u	- 1 u
After 1	42	3 u	72
Before 2	7 p	3 u	72
Change 2	- 1 p	+ 1 p
After 2	6 p (36)	36	72

Since Cindy gave some beads to Sabrina and Sabrina 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 Sabrina each had in the end is the same.

Number of beads that Sabrina had in the end
= 72 ÷ 2
= 36

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

6 p = 36

1 p = 36 ÷ 6 = 6

Number of beads that Sabrina had after receiving some beads from Cindy
= 7 p
= 7 x 6
= 42

Number of beads that Cindy had after giving to Sabrina
= 72 - 42
= 30

3 u = 30

1 u = 30 ÷ 3 = 10

Number of beads that Cindy had at first
= 4 u
= 4 x 10
= 40

Number of beads that Sabrina had at first
= 72 - 40
= 32

Answer(s): 32