Diana, Yen and Shannon were playing with beads. Diana started with 40 beads and in the first game, she won ³₅ more beads from Yen. In the second game, Diana lost ¹₈ of her original number of beads to Shannon. Yen lost as many beads as Diana to Shannon. In the final game, Diana won ¹₂ of her original number of beads from Yen. All of them ended up with the same number of beads.

1. How many beads did Diana have in the end?
2. How many beads did Yen have at first?

	Diana	Yen	Shannon
Before	40
First game	+ 24	- 24
Second game	- 5		+ 5
		- 5	+ 5
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Diana won from Yen
= ³₅ x 40
= 24

Number of beads that Diana lost to Shannon
= ¹₈ x 40
= 5

Number of beads that Diana won from Yen
= ¹₂ x 40
= 20

Number of beads that Diana had in the end
= 40 + 24 - 5 + 20
= 79

(b)
Number of beads that Yen had at first
= 1 u + 20 + 5 + 24
= 79 + 20 + 5 + 24
= 128 

Answer(s): (a) 79 ; (b) 128