Wesley had ³₄ as many beads as Archie. Archie had ⁴₇ as many beads as Shannon. After Wesley and Shannon gave 14 beads to Archie, Archie had thrice as many beads as Wesley. Shannon then had the same number of beads as Archie.

1. What was the ratio of the number of beads Wesley had to the number of beads Shannon had in the beginning? Answer in simplest form.
2. How many beads did Archie have in the end?

Wesley	Archie	Shannon
3	4
	4	7
3	4	7

(a)
The number of beads that Archie is repeated.  

Ratio of the number of beads that Wesley had to the number of beads that Shannon had in the beginning = 3 : 7

	Wesley	Archie	Shannon	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 14	+ 28	- 14
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of beads at first and in the end remains unchanged. Make the total number of beads the same. LCM of 14 and 7 is 14.

Number of beads that Archie received from Wesley and Shannon
= 2 x 14
= 28

Number of beads that Archie received from Wesley and Shannon
= 2 x 1 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

Number of beads that Ashley had in the end
= 6 u
= 6 x 7
= 42