Erika and Julie had a total of 60 beads. Julie gave ¹₃ of her beads to Erika. In return, Erika gave ¹₆ of the total number of beads that she had to Julie. In the end, each girl had the same number of beads. How many beads did Erika have at first?

	Erika	Julie	Total
Before 1	?	3 u	60
Change 1	+ 1 u	- 1 u
After 1	36	2 u	60
Before 2	6 p	2 u	60
Change 2	- 1 p	+ 1 p
After 2	5 p (30)	30	60

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

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

Number of beads that Erika had in the end
= 60 ÷ 2
= 30

Number of beads that Erika had in the end = 5 p

5 p = 30

1 p = 30 ÷ 5 = 6

Number of beads that Erika had after receiving some beads from Julie
= 6 p
= 6 x 6
= 36

Number of beads that Julie had after giving to Erika
= 60 - 36
= 24

2 u = 24

1 u = 24 ÷ 2 = 12

Number of beads that Julie had at first
= 3 u
= 3 x 12
= 36

Number of beads that Erika had at first
= 60 - 36
= 24

Answer(s): 24