Eric had ¹₂ as many marbles as Lee. Lee had ²₃ as many marbles as Vanessa. After Eric and Vanessa gave 10 marbles to Lee, Lee had four times as many marbles as Eric. Vanessa then had the same number of marbles as Lee.

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

Eric	Lee	Vanessa
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Eric had to the number of marbles that Vanessa had in the beginning = 1 : 3

	Eric	Lee	Vanessa	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 10	+ 20	- 10
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of marbles at first and in the end remains unchanged. Make the total number of marbles the same. LCM of 6 and 9 is 18.

Number of marbles that Lee received from Eric and Vanessa
= 2 x 10
= 20

Number of marbles that Lee received from Eric and Vanessa
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of marbles that Ashley had in the end
= 8 u
= 8 x 5
= 40