Ivory, Linda and Olivia were playing with beads. Ivory started with 28 beads and in the first game, she won ³₄ more beads from Linda. In the second game, Ivory lost ⁵₇ of her original number of beads to Olivia. Linda lost as many beads as Ivory to Olivia. In the final game, Ivory won ¹₄ of her original number of beads from Linda. 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 Linda have at first?

	Ivory	Linda	Olivia
Before	28
First game	+ 21	- 21
Second game	- 20		+ 20
		- 20	+ 20
Final game	+ 7	- 7
After	1 u	1 u	1 u

(a)
Number of beads that Ivory won from Linda
= ³₄ x 28
= 21

Number of beads that Ivory lost to Olivia
= ⁵₇ x 28
= 20

Number of beads that Ivory won from Linda
= ¹₄ x 28
= 7

Number of beads that Ivory had in the end
= 28 + 21 - 20 + 7
= 36

(b)
Number of beads that Linda had at first
= 1 u + 7 + 20 + 21
= 36 + 7 + 20 + 21
= 84 

Answer(s): (a) 36 ; (b) 84