Ken had ³₄ as many beads as Cody. Cody had ⁴₇ as many beads as Lucy. After Ken and Lucy gave 30 beads to Cody, Cody had thrice as many beads as Ken. Lucy then had the same number of beads as Cody.

1. What was the ratio of the number of beads Lucy had to the number of beads Ken had in the beginning? Answer in simplest form.
2. How many beads did Cody have in the end?

Ken	Cody	Lucy
3	4
	4	7
3	4	7

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

Ratio of the number of beads that Lucy had to the number of beads that Ken had in the beginning = 7 : 3

	Ken	Cody	Lucy	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 30	+ 60	- 30
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 Cody received from Ken and Lucy
= 2 x 30
= 60

Number of beads that Cody received from Ken and Lucy
= 2 x 1 u
= 2 u

2 u = 30

1 u = 30 ÷ 2 = 15

Number of beads that Ashley had in the end
= 6 u
= 6 x 15
= 90