Jenson, Jack and Ryan had a total of 69 pens. The ratio of Jack's pens to Ryan's pens was 2 : 7 at first. Jenson and Jack each gave away ¹₂ of their pens. Given that the three boys had 52 pens left, how many pens did Jenson have in the end?

	Jenson	Jack	Ryan	Total
Comparing Jack and Ryan at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	69
Change	- 1 p	-1x1 = - 1 u		- 17
After	1 p	1x1 = 1 u	7 u	52

Total number of pens that Jenson and Jack gave away
= 69 - 52
= 17

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

1 p + 1 u = 69 - 52
1 p + 1 u = 17
1 p = 17 - 1 u --- (1)

1 p + 1 u + 7 u = 52
1 p + 8 u = 52
1 p = 52 - 8 u --- (2)

(1) = (2)
17 - 1 u = 52 - 8 u
8 u - 1 u = 52 - 17
8 u - 1 u = 35
7 u = 35

1 u = 35 ÷ 7 = 5

Substitute 1 u = 5 into (1).
1 p = 17 - 1 u
1 p = 17 - 1 x 5
1 p = 17 - 5

1 p = 12

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

Answer(s): 12