Emma, Linda and Min were playing with beads. Emma started with 70 beads and in the first game, she won ⁴₅ more beads from Linda. In the second game, Emma lost ⁴₇ of her original number of beads to Min. Linda lost as many beads as Emma to Min. In the final game, Emma won ¹₂ of her original number of beads from Linda. All of them ended up with the same number of beads.

1. How many beads did Emma have in the end?
2. How many beads did Linda have at first?

	Emma	Linda	Min
Before	70
First game	+ 56	- 56
Second game	- 40		+ 40
		- 40	+ 40
Final game	+ 35	- 35
After	1 u	1 u	1 u

(a)
Number of beads that Emma won from Linda
= ⁴₅ x 70
= 56

Number of beads that Emma lost to Min
= ⁴₇ x 70
= 40

Number of beads that Emma won from Linda
= ¹₂ x 70
= 35

Number of beads that Emma had in the end
= 70 + 56 - 40 + 35
= 121

(b)
Number of beads that Linda had at first
= 1 u + 35 + 40 + 56
= 121 + 35 + 40 + 56
= 252 

Answer(s): (a) 121 ; (b) 252