Julie and Anna had a total of 168 beads. Anna gave ¹₄ of her beads to Julie. In return, Julie gave ¹₈ of the total number of beads that she had to Anna. In the end, each girl had the same number of beads. How many beads did Julie have at first?

	Julie	Anna	Total
Before 1	?	4 u	168
Change 1	+ 1 u	- 1 u
After 1	96	3 u	168
Before 2	8 p	3 u	168
Change 2	- 1 p	+ 1 p
After 2	7 p (84)	84	168

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

Number of beads that Anna and Julie each had in the end is the same.

Number of beads that Julie had in the end
= 168 ÷ 2
= 84

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

7 p = 84

1 p = 84 ÷ 7 = 12

Number of beads that Julie had after receiving some beads from Anna
= 8 p
= 8 x 12
= 96

Number of beads that Anna had after giving to Julie
= 168 - 96
= 72

3 u = 72

1 u = 72 ÷ 3 = 24

Number of beads that Anna had at first
= 4 u
= 4 x 24
= 96

Number of beads that Julie had at first
= 168 - 96
= 72

Answer(s): 72