Dylan had ³₄ as many pens as Ivan. Ivan had ⁴₇ as many pens as Lynn. After Dylan and Lynn gave 18 pens to Ivan, Ivan had thrice as many pens as Dylan. Lynn then had the same number of pens as Ivan.

1. What was the ratio of the number of pens Lynn had to the number of pens Dylan had in the beginning? Answer in simplest form.
2. How many pens did Ivan have in the end?

Dylan	Ivan	Lynn
3	4
	4	7
3	4	7

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

Ratio of the number of pens that Lynn had to the number of pens that Dylan had in the beginning = 7 : 3

	Dylan	Ivan	Lynn	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 18	+ 36	- 18
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 Ivan received from Dylan and Lynn
= 2 x 18
= 36

Number of pens that Ivan received from Dylan and Lynn
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of pens that Ashley had in the end
= 6 u
= 6 x 9
= 54