Emily and Min had a total of 28 beads. Min gave ¹₅ of her beads to Emily. In return, Emily gave ¹₈ of the total number of beads that she had to Min. In the end, each girl had the same number of beads. How many beads did Emily have at first?

	Emily	Min	Total
Before 1	?	5 u	28
Change 1	+ 1 u	- 1 u
After 1	16	4 u	28
Before 2	8 p	4 u	28
Change 2	- 1 p	+ 1 p
After 2	7 p (14)	14	28

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

Number of beads that Min and Emily each had in the end is the same.

Number of beads that Emily had in the end
= 28 ÷ 2
= 14

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

7 p = 14

1 p = 14 ÷ 7 = 2

Number of beads that Emily had after receiving some beads from Min
= 8 p
= 8 x 2
= 16

Number of beads that Min had after giving to Emily
= 28 - 16
= 12

4 u = 12

1 u = 12 ÷ 4 = 3

Number of beads that Min had at first
= 5 u
= 5 x 3
= 15

Number of beads that Emily had at first
= 28 - 15
= 13

Answer(s): 13