Zane, Luis and Bobby had a total of 97 stickers. The ratio of Luis's stickers to Bobby's stickers was 8 : 5 at first. Zane and Luis each gave away ¹₂ of their stickers. Given that the three boys had 66 stickers left, how many stickers did Zane have at first?

	Zane	Luis	Bobby	Total
Comparing Luis and Bobby at first		8 u	5 u
Before	2 p	2x4 = 8 u	5 u	97
Change	- 1 p	-1x4 = - 4 u		- 31
After	1 p	1x4 = 4 u	5 u	66

Total number of stickers that Zane and Luis gave away
= 97 - 66
= 31

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

1 p + 4 u = 97 - 66
1 p + 4 u = 31
1 p = 31 - 4 u --- (1)

1 p + 4 u + 5 u = 66
1 p + 9 u = 66
1 p = 66 - 9 u --- (2)

(1) = (2)
31 - 4 u = 66 - 9 u
9 u - 4 u = 66 - 31
9 u - 4 u = 35
5 u = 35

1 u = 35 ÷ 5 = 7

Substitute 1 u = 7 into (1).
1 p = 31 - 4 u
1 p = 31 - 4 x 7
1 p = 31 - 28

1 p = 3

Number of stickers that Zane had at first
= 2 p
= 2 x 3
= 6

Answer(s): 6