Neave had ³₄ as many pens as Fred. Fred had ⁴₇ as many pens as Gem. After Neave and Gem gave 16 pens to Fred, Fred had thrice as many pens as Neave. Gem then had the same number of pens as Fred.

1. What was the ratio of the number of pens Neave had to the number of pens Gem had in the beginning? Answer in simplest form.
2. How many pens did Fred have in the end?

Neave	Fred	Gem
3	4
	4	7
3	4	7

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

Ratio of the number of pens that Neave had to the number of pens that Gem had in the beginning = 3 : 7

	Neave	Fred	Gem	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 16	+ 32	- 16
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 Fred received from Neave and Gem
= 2 x 16
= 32

Number of pens that Fred received from Neave and Gem
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of pens that Ashley had in the end
= 6 u
= 6 x 8
= 48