Tom had ³₄ as many pens as Reggie. Reggie had ⁴₇ as many pens as Gillian. After Tom and Gillian gave 28 pens to Reggie, Reggie had thrice as many pens as Tom. Gillian then had the same number of pens as Reggie.

1. What was the ratio of the number of pens Tom had to the number of pens Gillian had in the beginning? Answer in simplest form.
2. How many pens did Reggie have in the end?

Tom	Reggie	Gillian
3	4
	4	7
3	4	7

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

Ratio of the number of pens that Tom had to the number of pens that Gillian had in the beginning = 3 : 7

	Tom	Reggie	Gillian	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
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 Reggie received from Tom and Gillian
= 2 x 28
= 56

Number of pens that Reggie received from Tom and Gillian
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of pens that Ashley had in the end
= 6 u
= 6 x 14
= 84