Reggie had ³₄ as many pens as Henry. Henry had ⁴₇ as many pens as Abi. After Reggie and Abi gave 24 pens to Henry, Henry had thrice as many pens as Reggie. Abi then had the same number of pens as Henry.

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

Reggie	Henry	Abi
3	4
	4	7
3	4	7

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

Ratio of the number of pens that Reggie had to the number of pens that Abi had in the beginning = 3 : 7

	Reggie	Henry	Abi	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 24	+ 48	- 24
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 Henry received from Reggie and Abi
= 2 x 24
= 48

Number of pens that Henry received from Reggie and Abi
= 2 x 1 u
= 2 u

2 u = 24

1 u = 24 ÷ 2 = 12

Number of pens that Ashley had in the end
= 6 u
= 6 x 12
= 72