Brandon, Asher and Michael had a total of 142 stickers. The ratio of Asher's stickers to Michael's stickers was 8 : 3 at first. Brandon and Asher each gave away ¹₂ of their stickers. Given that the three boys had 89 stickers left, how many stickers did Brandon have in the end?

	Brandon	Asher	Michael	Total
Comparing Asher and Michael at first		8 u	3 u
Before	2 p	2x4 = 8 u	3 u	142
Change	- 1 p	-1x4 = - 4 u		- 53
After	1 p	1x4 = 4 u	3 u	89

Total number of stickers that Brandon and Asher gave away
= 142 - 89
= 53

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

1 p + 4 u = 142 - 89
1 p + 4 u = 53
1 p = 53 - 4 u --- (1)

1 p + 4 u + 3 u = 89
1 p + 7 u = 89
1 p = 89 - 7 u --- (2)

(1) = (2)
53 - 4 u = 89 - 7 u
7 u - 4 u = 89 - 53
7 u - 4 u = 36
3 u = 36

1 u = 36 ÷ 3 = 12

Substitute 1 u = 12 into (1).
1 p = 53 - 4 u
1 p = 53 - 4 x 12
1 p = 53 - 48

1 p = 5

Number of stickers that Brandon had in the end
= 1 p
= 5

Answer(s): 5