Bobby, Jenson and Oliver had a total of 108 pens. The ratio of Jenson's pens to Oliver's pens was 8 : 7 at first. Bobby and Jenson each gave away ¹₂ of their pens. Given that the three boys had 75 pens left, how many pens did Bobby have in the end?

	Bobby	Jenson	Oliver	Total
Comparing Jenson and Oliver at first		8 u	7 u
Before	2 p	2x4 = 8 u	7 u	108
Change	- 1 p	-1x4 = - 4 u		- 33
After	1 p	1x4 = 4 u	7 u	75

Total number of pens that Bobby and Jenson gave away
= 108 - 75
= 33

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 8 and 2 is 8.

1 p + 4 u = 108 - 75
1 p + 4 u = 33
1 p = 33 - 4 u --- (1)

1 p + 4 u + 7 u = 75
1 p + 11 u = 75
1 p = 75 - 11 u --- (2)

(1) = (2)
33 - 4 u = 75 - 11 u
11 u - 4 u = 75 - 33
11 u - 4 u = 42
7 u = 42

1 u = 42 ÷ 7 = 6

Substitute 1 u = 6 into (1).
1 p = 33 - 4 u
1 p = 33 - 4 x 6
1 p = 33 - 24

1 p = 9

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

Answer(s): 9