Cody, Ethan and Jenson had a total of 77 pens. The ratio of Ethan's pens to Jenson's pens was 4 : 7 at first. Cody and Ethan each gave away ¹₂ of their pens. Given that the three boys had 56 pens left, how many pens did Cody have in the end?

	Cody	Ethan	Jenson	Total
Comparing Ethan and Jenson at first		4 u	7 u
Before	2 p	2x2 = 4 u	7 u	77
Change	- 1 p	-1x2 = - 2 u		- 21
After	1 p	1x2 = 2 u	7 u	56

Total number of pens that Cody and Ethan gave away
= 77 - 56
= 21

The number of pens that Ethan had at first is repeated.  Make the number of pens that Ethan had at first the same.  LCM of 4 and 2 is 4.

1 p + 2 u = 77 - 56
1 p + 2 u = 21
1 p = 21 - 2 u --- (1)

1 p + 2 u + 7 u = 56
1 p + 9 u = 56
1 p = 56 - 9 u --- (2)

(1) = (2)
21 - 2 u = 56 - 9 u
9 u - 2 u = 56 - 21
9 u - 2 u = 35
7 u = 35

1 u = 35 ÷ 7 = 5

Substitute 1 u = 5 into (1).
1 p = 21 - 2 u
1 p = 21 - 2 x 5
1 p = 21 - 10

1 p = 11

Number of pens that Cody had in the end
= 1 p
= 11

Answer(s): 11