Justin, Ivan and Ahmad had a total of 99 stickers. The ratio of Ivan's stickers to Ahmad's stickers was 6 : 5 at first. Justin and Ivan each gave away ¹₂ of their stickers. Given that the three boys had 67 stickers left, how many stickers did Justin have at first?

	Justin	Ivan	Ahmad	Total
Comparing Ivan and Ahmad at first		6 u	5 u
Before	2 p	2x3 = 6 u	5 u	99
Change	- 1 p	-1x3 = - 3 u		- 32
After	1 p	1x3 = 3 u	5 u	67

Total number of stickers that Justin and Ivan gave away
= 99 - 67
= 32

The number of stickers that Ivan had at first is repeated.  Make the number of stickers that Ivan had at first the same.  LCM of 6 and 2 is 6.

1 p + 3 u = 99 - 67
1 p + 3 u = 32
1 p = 32 - 3 u --- (1)

1 p + 3 u + 5 u = 67
1 p + 8 u = 67
1 p = 67 - 8 u --- (2)

(1) = (2)
32 - 3 u = 67 - 8 u
8 u - 3 u = 67 - 32
8 u - 3 u = 35
5 u = 35

1 u = 35 ÷ 5 = 7

Substitute 1 u = 7 into (1).
1 p = 32 - 3 u
1 p = 32 - 3 x 7
1 p = 32 - 21

1 p = 11

Number of stickers that Justin had at first
= 2 p
= 2 x 11
= 22

Answer(s): 22