Penelope, Zara and Dana were playing with beads. Penelope started with 35 beads and in the first game, she won ²₅ more beads from Zara. In the second game, Penelope lost ³₇ of her original number of beads to Dana. Zara lost as many beads as Penelope to Dana. In the final game, Penelope won ¹₅ of her original number of beads from Zara. All of them ended up with the same number of beads.

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

	Penelope	Zara	Dana
Before	35
First game	+ 14	- 14
Second game	- 15		+ 15
		- 15	+ 15
Final game	+ 7	- 7
After	1 u	1 u	1 u

(a)
Number of beads that Penelope won from Zara
= ²₅ x 35
= 14

Number of beads that Penelope lost to Dana
= ³₇ x 35
= 15

Number of beads that Penelope won from Zara
= ¹₅ x 35
= 7

Number of beads that Penelope had in the end
= 35 + 14 - 15 + 7
= 41

(b)
Number of beads that Zara had at first
= 1 u + 7 + 15 + 14
= 41 + 7 + 15 + 14
= 77 

Answer(s): (a) 41 ; (b) 77