Zara, Lucy and Emily were playing with beads. Zara started with 35 beads and in the first game, she won ²₅ more beads from Lucy. In the second game, Zara lost ⁶₇ of her original number of beads to Emily. Lucy lost as many beads as Zara to Emily. In the final game, Zara won ¹₅ of her original number of beads from Lucy. All of them ended up with the same number of beads.

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

	Zara	Lucy	Emily
Before	35
First game	+ 14	- 14
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 7	- 7
After	1 u	1 u	1 u

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

Number of beads that Zara lost to Emily
= ⁶₇ x 35
= 30

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

Number of beads that Zara had in the end
= 35 + 14 - 30 + 7
= 26

(b)
Number of beads that Lucy had at first
= 1 u + 7 + 30 + 14
= 26 + 7 + 30 + 14
= 77 

Answer(s): (a) 26 ; (b) 77