Xandra, Usha and Zara were playing with beads. Xandra started with 24 beads and in the first game, she won ¹₄ more beads from Usha. In the second game, Xandra lost ³₈ of her original number of beads to Zara. Usha lost as many beads as Xandra to Zara. In the final game, Xandra won ¹₃ of her original number of beads from Usha. All of them ended up with the same number of beads.

1. How many beads did Xandra have in the end?
2. How many beads did Usha have at first?

	Xandra	Usha	Zara
Before	24
First game	+ 6	- 6
Second game	- 9		+ 9
		- 9	+ 9
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Xandra won from Usha
= ¹₄ x 24
= 6

Number of beads that Xandra lost to Zara
= ³₈ x 24
= 9

Number of beads that Xandra won from Usha
= ¹₃ x 24
= 8

Number of beads that Xandra had in the end
= 24 + 6 - 9 + 8
= 29

(b)
Number of beads that Usha had at first
= 1 u + 8 + 9 + 6
= 29 + 8 + 9 + 6
= 52 

Answer(s): (a) 29 ; (b) 52