Anna, Hilda and Fiona were playing with beads. Anna started with 32 beads and in the first game, she won ¹₄ more beads from Hilda. In the second game, Anna lost ⁵₈ of her original number of beads to Fiona. Hilda lost as many beads as Anna to Fiona. In the final game, Anna won ¹₂ of her original number of beads from Hilda. All of them ended up with the same number of beads.

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

	Anna	Hilda	Fiona
Before	32
First game	+ 8	- 8
Second game	- 20		+ 20
		- 20	+ 20
Final game	+ 16	- 16
After	1 u	1 u	1 u

(a)
Number of beads that Anna won from Hilda
= ¹₄ x 32
= 8

Number of beads that Anna lost to Fiona
= ⁵₈ x 32
= 20

Number of beads that Anna won from Hilda
= ¹₂ x 32
= 16

Number of beads that Anna had in the end
= 32 + 8 - 20 + 16
= 36

(b)
Number of beads that Hilda had at first
= 1 u + 16 + 20 + 8
= 36 + 16 + 20 + 8
= 80 

Answer(s): (a) 36 ; (b) 80