Valen had ³₄ as many stamps as Eric. Eric had ⁴₇ as many stamps as Penelope. After Valen and Penelope gave 20 stamps to Eric, Eric had thrice as many stamps as Valen. Penelope then had the same number of stamps as Eric.

1. What was the ratio of the number of stamps Penelope had to the number of stamps Valen had in the beginning? Answer in simplest form.
2. How many stamps did Eric have in the end?

Valen	Eric	Penelope
3	4
	4	7
3	4	7

(a)
The number of stamps that Eric is repeated.  

Ratio of the number of stamps that Penelope had to the number of stamps that Valen had in the beginning = 7 : 3

	Valen	Eric	Penelope	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 stamps at first and in the end remains unchanged. Make the total number of stamps the same. LCM of 14 and 7 is 14.

Number of stamps that Eric received from Valen and Penelope
= 2 x 20
= 40

Number of stamps that Eric received from Valen and Penelope
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

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