Gillian and Nicole had a total of 56 beads. Nicole gave ¹₄ of her beads to Gillian. In return, Gillian gave ¹₈ of the total number of beads that she had to Nicole. In the end, each girl had the same number of beads. How many beads did Gillian have at first?

	Gillian	Nicole	Total
Before 1	?	4 u	56
Change 1	+ 1 u	- 1 u
After 1	32	3 u	56
Before 2	8 p	3 u	56
Change 2	- 1 p	+ 1 p
After 2	7 p (28)	28	56

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

Number of beads that Nicole and Gillian each had in the end is the same.

Number of beads that Gillian had in the end
= 56 ÷ 2
= 28

Number of beads that Gillian had in the end = 7 p

7 p = 28

1 p = 28 ÷ 7 = 4

Number of beads that Gillian had after receiving some beads from Nicole
= 8 p
= 8 x 4
= 32

Number of beads that Nicole had after giving to Gillian
= 56 - 32
= 24

3 u = 24

1 u = 24 ÷ 3 = 8

Number of beads that Nicole had at first
= 4 u
= 4 x 8
= 32

Number of beads that Gillian had at first
= 56 - 32
= 24

Answer(s): 24