Anna, Joelle and Tammy were playing with beads. Anna started with 40 beads and in the first game, she won ²₅ more beads from Joelle. In the second game, Anna lost ¹₈ of her original number of beads to Tammy. Joelle lost as many beads as Anna to Tammy. In the final game, Anna won ¹₂ of her original number of beads from Joelle. All of them ended up with the same number of beads.

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

	Anna	Joelle	Tammy
Before	40
First game	+ 16	- 16
Second game	- 5		+ 5
		- 5	+ 5
Final game	+ 20	- 20
After	1 u	1 u	1 u

(a)
Number of beads that Anna won from Joelle
= ²₅ x 40
= 16

Number of beads that Anna lost to Tammy
= ¹₈ x 40
= 5

Number of beads that Anna won from Joelle
= ¹₂ x 40
= 20

Number of beads that Anna had in the end
= 40 + 16 - 5 + 20
= 71

(b)
Number of beads that Joelle had at first
= 1 u + 20 + 5 + 16
= 71 + 20 + 5 + 16
= 112 

Answer(s): (a) 71 ; (b) 112