Jane and Julie had a total of 24 beads. Julie gave ¹₅ of her beads to Jane. In return, Jane gave ¹₄ 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 Jane have at first?

	Jane	Julie	Total
Before 1	?	5 u	24
Change 1	+ 1 u	- 1 u
After 1	16	4 u	24
Before 2	4 p	4 u	24
Change 2	- 1 p	+ 1 p
After 2	3 p (12)	12	24

Since Julie gave some beads to Jane and Jane 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 Jane each had in the end is the same.

Number of beads that Jane had in the end
= 24 ÷ 2
= 12

Number of beads that Jane had in the end = 3 p

3 p = 12

1 p = 12 ÷ 3 = 4

Number of beads that Jane had after receiving some beads from Julie
= 4 p
= 4 x 4
= 16

Number of beads that Julie had after giving to Jane
= 24 - 16
= 8

4 u = 8

1 u = 8 ÷ 4 = 2

Number of beads that Julie had at first
= 5 u
= 5 x 2
= 10

Number of beads that Jane had at first
= 24 - 10
= 14

Answer(s): 14