Mary, Kathy and Erika were playing with beads. Mary started with 56 beads and in the first game, she won ¹₄ more beads from Kathy. In the second game, Mary lost ⁴₇ of her original number of beads to Erika. Kathy lost as many beads as Mary to Erika. In the final game, Mary won ¹₂ of her original number of beads from Kathy. All of them ended up with the same number of beads.

1. How many beads did Mary have in the end?
2. How many beads did Kathy have at first?

	Mary	Kathy	Erika
Before	56
First game	+ 14	- 14
Second game	- 32		+ 32
		- 32	+ 32
Final game	+ 28	- 28
After	1 u	1 u	1 u

(a)
Number of beads that Mary won from Kathy
= ¹₄ x 56
= 14

Number of beads that Mary lost to Erika
= ⁴₇ x 56
= 32

Number of beads that Mary won from Kathy
= ¹₂ x 56
= 28

Number of beads that Mary had in the end
= 56 + 14 - 32 + 28
= 66

(b)
Number of beads that Kathy had at first
= 1 u + 28 + 32 + 14
= 66 + 28 + 32 + 14
= 140 

Answer(s): (a) 66 ; (b) 140