Nora, Hilda and Jane were playing with beads. Nora started with 40 beads and in the first game, she won ³₅ more beads from Hilda. In the second game, Nora lost ¹₈ of her original number of beads to Jane. Hilda lost as many beads as Nora to Jane. In the final game, Nora won ¹₅ of her original number of beads from Hilda. All of them ended up with the same number of beads.

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

	Nora	Hilda	Jane
Before	40
First game	+ 24	- 24
Second game	- 5		+ 5
		- 5	+ 5
Final game	+ 8	- 8
After	1 u	1 u	1 u

(a)
Number of beads that Nora won from Hilda
= ³₅ x 40
= 24

Number of beads that Nora lost to Jane
= ¹₈ x 40
= 5

Number of beads that Nora won from Hilda
= ¹₅ x 40
= 8

Number of beads that Nora had in the end
= 40 + 24 - 5 + 8
= 67

(b)
Number of beads that Hilda had at first
= 1 u + 8 + 5 + 24
= 67 + 8 + 5 + 24
= 104 

Answer(s): (a) 67 ; (b) 104