Caden, Riordan and Jenson had a total of 61 stickers. The ratio of Riordan's stickers to Jenson's stickers was 8 : 7 at first. Caden and Riordan each gave away ¹₂ of their stickers. Given that the three boys had 41 stickers left, how many stickers did Caden have in the end?

	Caden	Riordan	Jenson	Total
Comparing Riordan and Jenson at first		8 u	7 u
Before	2 p	2x4 = 8 u	7 u	61
Change	- 1 p	-1x4 = - 4 u		- 20
After	1 p	1x4 = 4 u	7 u	41

Total number of stickers that Caden and Riordan gave away
= 61 - 41
= 20

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

1 p + 4 u = 61 - 41
1 p + 4 u = 20
1 p = 20 - 4 u --- (1)

1 p + 4 u + 7 u = 41
1 p + 11 u = 41
1 p = 41 - 11 u --- (2)

(1) = (2)
20 - 4 u = 41 - 11 u
11 u - 4 u = 41 - 20
11 u - 4 u = 21
7 u = 21

1 u = 21 ÷ 7 = 3

Substitute 1 u = 3 into (1).
1 p = 20 - 4 u
1 p = 20 - 4 x 3
1 p = 20 - 12

1 p = 8

Number of stickers that Caden had in the end
= 1 p
= 8

Answer(s): 8