Barbara, Anna and Nora were playing with beads. Barbara started with 72 beads and in the first game, she won ¹₃ more beads from Anna. In the second game, Barbara lost ³₈ of her original number of beads to Nora. Anna lost as many beads as Barbara to Nora. In the final game, Barbara won ¹₄ of her original number of beads from Anna. All of them ended up with the same number of beads.

1. How many beads did Barbara have in the end?
2. How many beads did Anna have at first?

	Barbara	Anna	Nora
Before	72
First game	+ 24	- 24
Second game	- 27		+ 27
		- 27	+ 27
Final game	+ 18	- 18
After	1 u	1 u	1 u

(a)
Number of beads that Barbara won from Anna
= ¹₃ x 72
= 24

Number of beads that Barbara lost to Nora
= ³₈ x 72
= 27

Number of beads that Barbara won from Anna
= ¹₄ x 72
= 18

Number of beads that Barbara had in the end
= 72 + 24 - 27 + 18
= 87

(b)
Number of beads that Anna had at first
= 1 u + 18 + 27 + 24
= 87 + 18 + 27 + 24
= 156 

Answer(s): (a) 87 ; (b) 156