Mary, Xuan and Jade were playing with beads. Mary started with 40 beads and in the first game, she won ³₄ more beads from Xuan. In the second game, Mary lost ¹₈ of her original number of beads to Jade. Xuan lost as many beads as Mary to Jade. In the final game, Mary won ¹₂ of her original number of beads from Xuan. All of them ended up with the same number of beads.

1. How many beads did Mary have in the end?
2. How many beads did Xuan have at first?

	Mary	Xuan	Jade
Before	40
First game	+ 30	- 30
Second game	- 5		+ 5
		- 5	+ 5
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Mary won from Xuan
= ³₄ x 40
= 30

Number of beads that Mary lost to Jade
= ¹₈ x 40
= 5

Number of beads that Mary won from Xuan
= ¹₂ x 40
= 20

Number of beads that Mary had in the end
= 40 + 30 - 5 + 20
= 85

(b)
Number of beads that Xuan had at first
= 1 u + 20 + 5 + 30
= 85 + 20 + 5 + 30
= 140 

Answer(s): (a) 85 ; (b) 140