Caden had ³₄ as many marbles as Lee. Lee had ⁴₇ as many marbles as Gillian. After Caden and Gillian gave 28 marbles to Lee, Lee had thrice as many marbles as Caden. Gillian then had the same number of marbles as Lee.

1. What was the ratio of the number of marbles Caden had to the number of marbles Gillian had in the beginning? Answer in simplest form.
2. How many marbles did Lee have in the end?

Caden	Lee	Gillian
3	4
	4	7
3	4	7

(a)
The number of marbles that Lee is repeated.  

Ratio of the number of marbles that Caden had to the number of marbles that Gillian had in the beginning = 3 : 7

	Caden	Lee	Gillian	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

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

Number of marbles that Lee received from Caden and Gillian
= 2 x 28
= 56

Number of marbles that Lee received from Caden and Gillian
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of marbles that Ashley had in the end
= 6 u
= 6 x 14
= 84