Vaidev had ³₄ as many pens as Eric. Eric had ⁴₇ as many pens as Nicole. After Vaidev and Nicole gave 14 pens to Eric, Eric had thrice as many pens as Vaidev. Nicole then had the same number of pens as Eric.

1. What was the ratio of the number of pens Vaidev had to the number of pens Nicole had in the beginning? Answer in simplest form.
2. How many pens did Eric have in the end?

Vaidev	Eric	Nicole
3	4
	4	7
3	4	7

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

Ratio of the number of pens that Vaidev had to the number of pens that Nicole had in the beginning = 3 : 7

	Vaidev	Eric	Nicole	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 14	+ 28	- 14
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

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

Number of pens that Eric received from Vaidev and Nicole
= 2 x 14
= 28

Number of pens that Eric received from Vaidev and Nicole
= 2 x 1 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

Number of pens that Ashley had in the end
= 6 u
= 6 x 7
= 42