Mary, Natalie and Kathy were playing with beads. Mary started with 84 beads and in the first game, she won ¹₃ more beads from Natalie. In the second game, Mary lost ⁵₇ of her original number of beads to Kathy. Natalie lost as many beads as Mary to Kathy. In the final game, Mary won ¹₄ of her original number of beads from Natalie. 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 Natalie have at first?

	Mary	Natalie	Kathy
Before	84
First game	+ 28	- 28
Second game	- 60		+ 60
		- 60	+ 60
Final game	+ 21	- 21
After	1 u	1 u	1 u

(a)
Number of beads that Mary won from Natalie
= ¹₃ x 84
= 28

Number of beads that Mary lost to Kathy
= ⁵₇ x 84
= 60

Number of beads that Mary won from Natalie
= ¹₄ x 84
= 21

Number of beads that Mary had in the end
= 84 + 28 - 60 + 21
= 73

(b)
Number of beads that Natalie had at first
= 1 u + 21 + 60 + 28
= 73 + 21 + 60 + 28
= 182 

Answer(s): (a) 73 ; (b) 182