Henry, Carl and Tom had a total of 118 stickers. The ratio of Carl's stickers to Tom's stickers was 2 : 9 at first. Henry and Carl each gave away ¹₂ of their stickers. Given that the three boys had 104 stickers left, how many stickers did Henry have at first?

	Henry	Carl	Tom	Total
Comparing Carl and Tom at first		2 u	9 u
Before	2 p	2x1 = 2 u	9 u	118
Change	- 1 p	-1x1 = - 1 u		- 14
After	1 p	1x1 = 1 u	9 u	104

Total number of stickers that Henry and Carl gave away
= 118 - 104
= 14

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

1 p + 1 u = 118 - 104
1 p + 1 u = 14
1 p = 14 - 1 u --- (1)

1 p + 1 u + 9 u = 104
1 p + 10 u = 104
1 p = 104 - 10 u --- (2)

(1) = (2)
14 - 1 u = 104 - 10 u
10 u - 1 u = 104 - 14
10 u - 1 u = 90
9 u = 90

1 u = 90 ÷ 9 = 10

Substitute 1 u = 10 into (1).
1 p = 14 - 1 u
1 p = 14 - 1 x 10
1 p = 14 - 10

1 p = 4

Number of stickers that Henry had at first
= 2 p
= 2 x 4
= 8

Answer(s): 8