Xandra, Jean and Nora were playing with beads. Xandra started with 40 beads and in the first game, she won ¹₂ more beads from Jean. In the second game, Xandra lost ³₈ of her original number of beads to Nora. Jean lost as many beads as Xandra to Nora. In the final game, Xandra won ¹₄ of her original number of beads from Jean. 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 Jean have at first?

	Xandra	Jean	Nora
Before	40
First game	+ 20	- 20
Second game	- 15		+ 15
		- 15	+ 15
Final game	+ 10	- 10
After	1 u	1 u	1 u

(a)
Number of beads that Xandra won from Jean
= ¹₂ x 40
= 20

Number of beads that Xandra lost to Nora
= ³₈ x 40
= 15

Number of beads that Xandra won from Jean
= ¹₄ x 40
= 10

Number of beads that Xandra had in the end
= 40 + 20 - 15 + 10
= 55

(b)
Number of beads that Jean had at first
= 1 u + 10 + 15 + 20
= 55 + 10 + 15 + 20
= 100 

Answer(s): (a) 55 ; (b) 100