Xandra and Risa had a total of 112 beads. Risa gave ¹₄ of her beads to Xandra. In return, Xandra gave ¹₈ of the total number of beads that she had to Risa. In the end, each girl had the same number of beads. How many beads did Xandra have at first?

	Xandra	Risa	Total
Before 1	?	4 u	112
Change 1	+ 1 u	- 1 u
After 1	64	3 u	112
Before 2	8 p	3 u	112
Change 2	- 1 p	+ 1 p
After 2	7 p (56)	56	112

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

Number of beads that Risa and Xandra each had in the end is the same.

Number of beads that Xandra had in the end
= 112 ÷ 2
= 56

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

7 p = 56

1 p = 56 ÷ 7 = 8

Number of beads that Xandra had after receiving some beads from Risa
= 8 p
= 8 x 8
= 64

Number of beads that Risa had after giving to Xandra
= 112 - 64
= 48

3 u = 48

1 u = 48 ÷ 3 = 16

Number of beads that Risa had at first
= 4 u
= 4 x 16
= 64

Number of beads that Xandra had at first
= 112 - 64
= 48

Answer(s): 48