Hilda, Xylia and Rachel were playing with beads. Hilda started with 24 beads and in the first game, she won ²₃ more beads from Xylia. In the second game, Hilda lost ³₈ of her original number of beads to Rachel. Xylia lost as many beads as Hilda to Rachel. In the final game, Hilda won ¹₃ of her original number of beads from Xylia. All of them ended up with the same number of beads.

1. How many beads did Hilda have in the end?
2. How many beads did Xylia have at first?

	Hilda	Xylia	Rachel
Before	24
First game	+ 16	- 16
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Hilda won from Xylia
= ²₃ x 24
= 16

Number of beads that Hilda lost to Rachel
= ³₈ x 24
= 9

Number of beads that Hilda won from Xylia
= ¹₃ x 24
= 8

Number of beads that Hilda had in the end
= 24 + 16 - 9 + 8
= 39

(b)
Number of beads that Xylia had at first
= 1 u + 8 + 9 + 16
= 39 + 8 + 9 + 16
= 72 

Answer(s): (a) 39 ; (b) 72