Hilda, Fanny and Tammy were playing with beads. Hilda started with 24 beads and in the first game, she won ¹₃ more beads from Fanny. In the second game, Hilda lost ¹₈ of her original number of beads to Tammy. Fanny lost as many beads as Hilda to Tammy. In the final game, Hilda won ¹₂ of her original number of beads from Fanny. All of them ended up with the same number of beads.

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

	Hilda	Fanny	Tammy
Before	24
First game	+ 8	- 8
Second game	- 3		+ 3
		- 3	+ 3
Final game	+ 12	- 12
After	1 u	1 u	1 u

(a)
Number of beads that Hilda won from Fanny
= ¹₃ x 24
= 8

Number of beads that Hilda lost to Tammy
= ¹₈ x 24
= 3

Number of beads that Hilda won from Fanny
= ¹₂ x 24
= 12

Number of beads that Hilda had in the end
= 24 + 8 - 3 + 12
= 41

(b)
Number of beads that Fanny had at first
= 1 u + 12 + 3 + 8
= 41 + 12 + 3 + 8
= 64 

Answer(s): (a) 41 ; (b) 64