Vaidev had ³₄ as many marbles as Valen. Valen had ⁴₇ as many marbles as Vanessa. After Vaidev and Vanessa gave 20 marbles to Valen, Valen had thrice as many marbles as Vaidev. Vanessa then had the same number of marbles as Valen.

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

Vaidev	Valen	Vanessa
3	4
	4	7
3	4	7

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

Ratio of the number of marbles that Vanessa had to the number of marbles that Vaidev had in the beginning = 7 : 3

	Vaidev	Valen	Vanessa	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 20	+ 40	- 20
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 Valen received from Vaidev and Vanessa
= 2 x 20
= 40

Number of marbles that Valen received from Vaidev and Vanessa
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of marbles that Ashley had in the end
= 6 u
= 6 x 10
= 60