Andy had ³₄ as many pens as Henry. Henry had ⁴₇ as many pens as Jade. After Andy and Jade gave 10 pens to Henry, Henry had thrice as many pens as Andy. Jade then had the same number of pens as Henry.

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

Andy	Henry	Jade
3	4
	4	7
3	4	7

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

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

	Andy	Henry	Jade	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 10	+ 20	- 10
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 Andy and Jade
= 2 x 10
= 20

Number of pens that Henry received from Andy and Jade
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of pens that Ashley had in the end
= 6 u
= 6 x 5
= 30