Kimberly and Joelle had a total of 48 beads. Joelle gave ¹₃ of her beads to Kimberly. In return, Kimberly gave ¹₅ of the total number of beads that she had to Joelle. In the end, each girl had the same number of beads. How many beads did Kimberly have at first?

	Kimberly	Joelle	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	30	2 u	48
Before 2	5 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	4 p (24)	24	48

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

Number of beads that Joelle and Kimberly each had in the end is the same.

Number of beads that Kimberly had in the end
= 48 ÷ 2
= 24

Number of beads that Kimberly had in the end = 4 p

4 p = 24

1 p = 24 ÷ 4 = 6

Number of beads that Kimberly had after receiving some beads from Joelle
= 5 p
= 5 x 6
= 30

Number of beads that Joelle had after giving to Kimberly
= 48 - 30
= 18

2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads that Joelle had at first
= 3 u
= 3 x 9
= 27

Number of beads that Kimberly had at first
= 48 - 27
= 21

Answer(s): 21