Harry, Sam and Ryan had a total of 201 pens. The ratio of Sam's pens to Ryan's pens was 8 : 9 at first. Harry and Sam each gave away ¹₂ of their pens. Given that the three boys had 150 pens left, how many pens did Harry have at first?

	Harry	Sam	Ryan	Total
Comparing Sam and Ryan at first		8 u	9 u
Before	2 p	2x4 = 8 u	9 u	201
Change	- 1 p	-1x4 = - 4 u		- 51
After	1 p	1x4 = 4 u	9 u	150

Total number of pens that Harry and Sam gave away
= 201 - 150
= 51

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

1 p + 4 u = 201 - 150
1 p + 4 u = 51
1 p = 51 - 4 u --- (1)

1 p + 4 u + 9 u = 150
1 p + 13 u = 150
1 p = 150 - 13 u --- (2)

(1) = (2)
51 - 4 u = 150 - 13 u
13 u - 4 u = 150 - 51
13 u - 4 u = 99
9 u = 99

1 u = 99 ÷ 9 = 11

Substitute 1 u = 11 into (1).
1 p = 51 - 4 u
1 p = 51 - 4 x 11
1 p = 51 - 44

1 p = 7

Number of pens that Harry had at first
= 2 p
= 2 x 7
= 14

Answer(s): 14