Flynn, Luke and Ivan had a total of 95 pens. The ratio of Luke's pens to Ivan's pens was 8 : 3 at first. Flynn and Luke each gave away ¹₂ of their pens. Given that the three boys had 58 pens left, how many pens did Flynn have in the end?

	Flynn	Luke	Ivan	Total
Comparing Luke and Ivan at first		8 u	3 u
Before	2 p	2x4 = 8 u	3 u	95
Change	- 1 p	-1x4 = - 4 u		- 37
After	1 p	1x4 = 4 u	3 u	58

Total number of pens that Flynn and Luke gave away
= 95 - 58
= 37

The number of pens that Luke had at first is repeated.  Make the number of pens that Luke had at first the same.  LCM of 8 and 2 is 8.

1 p + 4 u = 95 - 58
1 p + 4 u = 37
1 p = 37 - 4 u --- (1)

1 p + 4 u + 3 u = 58
1 p + 7 u = 58
1 p = 58 - 7 u --- (2)

(1) = (2)
37 - 4 u = 58 - 7 u
7 u - 4 u = 58 - 37
7 u - 4 u = 21
3 u = 21

1 u = 21 ÷ 3 = 7

Substitute 1 u = 7 into (1).
1 p = 37 - 4 u
1 p = 37 - 4 x 7
1 p = 37 - 28

1 p = 9

Number of pens that Flynn had in the end
= 1 p
= 9

Answer(s): 9