Emma, Xuan and Fiona were playing with beads. Emma started with 42 beads and in the first game, she won ¹₂ more beads from Xuan. In the second game, Emma lost ⁴₇ of her original number of beads to Fiona. Xuan lost as many beads as Emma to Fiona. In the final game, Emma won ¹₃ of her original number of beads from Xuan. All of them ended up with the same number of beads.

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

	Emma	Xuan	Fiona
Before	42
First game	+ 21	- 21
Second game	- 24		+ 24
		- 24	+ 24
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Emma won from Xuan
= ¹₂ x 42
= 21

Number of beads that Emma lost to Fiona
= ⁴₇ x 42
= 24

Number of beads that Emma won from Xuan
= ¹₃ x 42
= 14

Number of beads that Emma had in the end
= 42 + 21 - 24 + 14
= 53

(b)
Number of beads that Xuan had at first
= 1 u + 14 + 24 + 21
= 53 + 14 + 24 + 21
= 112 

Answer(s): (a) 53 ; (b) 112