Mary, Eva and Marion were playing with beads. Mary started with 42 beads and in the first game, she won ¹₂ more beads from Eva. In the second game, Mary lost ⁵₇ of her original number of beads to Marion. Eva lost as many beads as Mary to Marion. In the final game, Mary won ¹₃ of her original number of beads from Eva. 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 Eva have at first?

	Mary	Eva	Marion
Before	42
First game	+ 21	- 21
Second game	- 30		+ 30
		- 30	+ 30
Final game	+ 14	- 14
After	1 u	1 u	1 u

(a)
Number of beads that Mary won from Eva
= ¹₂ x 42
= 21

Number of beads that Mary lost to Marion
= ⁵₇ x 42
= 30

Number of beads that Mary won from Eva
= ¹₃ x 42
= 14

Number of beads that Mary had in the end
= 42 + 21 - 30 + 14
= 47

(b)
Number of beads that Eva had at first
= 1 u + 14 + 30 + 21
= 47 + 14 + 30 + 21
= 112 

Answer(s): (a) 47 ; (b) 112