Winnie and Ivory had a total of 80 beads. Ivory gave ¹₆ of her beads to Winnie. In return, Winnie gave ¹₅ of the total number of beads that she had to Ivory. In the end, each girl had the same number of beads. How many beads did Winnie have at first?

	Winnie	Ivory	Total
Before 1	?	6 u	80
Change 1	+ 1 u	- 1 u
After 1	50	5 u	80
Before 2	5 p	5 u	80
Change 2	- 1 p	+ 1 p
After 2	4 p (40)	40	80

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

Number of beads that Ivory and Winnie each had in the end is the same.

Number of beads that Winnie had in the end
= 80 ÷ 2
= 40

Number of beads that Winnie had in the end = 4 p

4 p = 40

1 p = 40 ÷ 4 = 10

Number of beads that Winnie had after receiving some beads from Ivory
= 5 p
= 5 x 10
= 50

Number of beads that Ivory had after giving to Winnie
= 80 - 50
= 30

5 u = 30

1 u = 30 ÷ 5 = 6

Number of beads that Ivory had at first
= 6 u
= 6 x 6
= 36

Number of beads that Winnie had at first
= 80 - 36
= 44

Answer(s): 44