Ahmad, Julian and Andy had a total of 60 pens. The ratio of Julian's pens to Andy's pens was 2 : 7 at first. Ahmad and Julian each gave away ¹₂ of their pens. Given that the three boys had 44 pens left, how many pens did Ahmad have in the end?

	Ahmad	Julian	Andy	Total
Comparing Julian and Andy at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	60
Change	- 1 p	-1x1 = - 1 u		- 16
After	1 p	1x1 = 1 u	7 u	44

Total number of pens that Ahmad and Julian gave away
= 60 - 44
= 16

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

1 p + 1 u = 60 - 44
1 p + 1 u = 16
1 p = 16 - 1 u --- (1)

1 p + 1 u + 7 u = 44
1 p + 8 u = 44
1 p = 44 - 8 u --- (2)

(1) = (2)
16 - 1 u = 44 - 8 u
8 u - 1 u = 44 - 16
8 u - 1 u = 28
7 u = 28

1 u = 28 ÷ 7 = 4

Substitute 1 u = 4 into (1).
1 p = 16 - 1 u
1 p = 16 - 1 x 4
1 p = 16 - 4

1 p = 12

Number of pens that Ahmad had in the end
= 1 p
= 12

Answer(s): 12