Ivory, Penelope and Hilda were playing with beads. Ivory started with 42 beads and in the first game, she won ¹₂ more beads from Penelope. In the second game, Ivory lost ⁵₇ of her original number of beads to Hilda. Penelope lost as many beads as Ivory to Hilda. In the final game, Ivory won ¹₃ of her original number of beads from Penelope. All of them ended up with the same number of beads.

1. How many beads did Ivory have in the end?
2. How many beads did Penelope have at first?

	Ivory	Penelope	Hilda
Before	42
First game	+ 21	- 21
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Ivory won from Penelope
= ¹₂ x 42
= 21

Number of beads that Ivory lost to Hilda
= ⁵₇ x 42
= 30

Number of beads that Ivory won from Penelope
= ¹₃ x 42
= 14

Number of beads that Ivory had in the end
= 42 + 21 - 30 + 14
= 47

(b)
Number of beads that Penelope had at first
= 1 u + 14 + 30 + 21
= 47 + 14 + 30 + 21
= 112 

Answer(s): (a) 47 ; (b) 112