Ivory and Nora had a total of 120 beads. Nora gave ¹₃ of her beads to Ivory. In return, Ivory gave ¹₇ of the total number of beads that she had to Nora. In the end, each girl had the same number of beads. How many beads did Ivory have at first?

	Ivory	Nora	Total
Before 1	?	3 u	120
Change 1	+ 1 u	- 1 u
After 1	70	2 u	120
Before 2	7 p	2 u	120
Change 2	- 1 p	+ 1 p
After 2	6 p (60)	60	120

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

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

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

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

6 p = 60

1 p = 60 ÷ 6 = 10

Number of beads that Ivory had after receiving some beads from Nora
= 7 p
= 7 x 10
= 70

Number of beads that Nora had after giving to Ivory
= 120 - 70
= 50

2 u = 50

1 u = 50 ÷ 2 = 25

Number of beads that Nora had at first
= 3 u
= 3 x 25
= 75

Number of beads that Ivory had at first
= 120 - 75
= 45

Answer(s): 45