Neave had ³₄ as many pens as Luis. Luis had ⁴₇ as many pens as Jade. After Neave and Jade gave 12 pens to Luis, Luis had thrice as many pens as Neave. Jade then had the same number of pens as Luis.

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

Neave	Luis	Jade
3	4
	4	7
3	4	7

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

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

	Neave	Luis	Jade	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 12	+ 24	- 12
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 Luis received from Neave and Jade
= 2 x 12
= 24

Number of pens that Luis received from Neave and Jade
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of pens that Ashley had in the end
= 6 u
= 6 x 6
= 36