Shiyun, Hilda and Zoe were playing with beads. Shiyun started with 84 beads and in the first game, she won ¹₂ more beads from Hilda. In the second game, Shiyun lost ⁴₇ of her original number of beads to Zoe. Hilda lost as many beads as Shiyun to Zoe. In the final game, Shiyun won ¹₄ of her original number of beads from Hilda. All of them ended up with the same number of beads.

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

	Shiyun	Hilda	Zoe
Before	84
First game	+ 42	- 42
Second game	- 48		+ 48
		- 48	+ 48
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Shiyun won from Hilda
= ¹₂ x 84
= 42

Number of beads that Shiyun lost to Zoe
= ⁴₇ x 84
= 48

Number of beads that Shiyun won from Hilda
= ¹₄ x 84
= 21

Number of beads that Shiyun had in the end
= 84 + 42 - 48 + 21
= 99

(b)
Number of beads that Hilda had at first
= 1 u + 21 + 48 + 42
= 99 + 21 + 48 + 42
= 210 

Answer(s): (a) 99 ; (b) 210