Seth, Jenson and George had a total of 127 pens. The ratio of Jenson's pens to George's pens was 4 : 7 at first. Seth and Jenson each gave away ¹₂ of their pens. Given that the three boys had 102 pens left, how many pens did Seth have in the end?

	Seth	Jenson	George	Total
Comparing Jenson and George at first		4 u	7 u
Before	2 p	2x2 = 4 u	7 u	127
Change	- 1 p	-1x2 = - 2 u		- 25
After	1 p	1x2 = 2 u	7 u	102

Total number of pens that Seth and Jenson gave away
= 127 - 102
= 25

The number of pens that Jenson had at first is repeated.  Make the number of pens that Jenson had at first the same.  LCM of 4 and 2 is 4.

1 p + 2 u = 127 - 102
1 p + 2 u = 25
1 p = 25 - 2 u --- (1)

1 p + 2 u + 7 u = 102
1 p + 9 u = 102
1 p = 102 - 9 u --- (2)

(1) = (2)
25 - 2 u = 102 - 9 u
9 u - 2 u = 102 - 25
9 u - 2 u = 77
7 u = 77

1 u = 77 ÷ 7 = 11

Substitute 1 u = 11 into (1).
1 p = 25 - 2 u
1 p = 25 - 2 x 11
1 p = 25 - 22

1 p = 3

Number of pens that Seth had in the end
= 1 p
= 3

Answer(s): 3