Tim, Fabian and Oliver had a total of 49 stickers. The ratio of Fabian's stickers to Oliver's stickers was 2 : 7 at first. Tim and Fabian each gave away ¹₂ of their stickers. Given that the three boys had 35 stickers left, how many stickers did Tim have in the end?

	Tim	Fabian	Oliver	Total
Comparing Fabian and Oliver at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	49
Change	- 1 p	-1x1 = - 1 u		- 14
After	1 p	1x1 = 1 u	7 u	35

Total number of stickers that Tim and Fabian gave away
= 49 - 35
= 14

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

1 p + 1 u = 49 - 35
1 p + 1 u = 14
1 p = 14 - 1 u --- (1)

1 p + 1 u + 7 u = 35
1 p + 8 u = 35
1 p = 35 - 8 u --- (2)

(1) = (2)
14 - 1 u = 35 - 8 u
8 u - 1 u = 35 - 14
8 u - 1 u = 21
7 u = 21

1 u = 21 ÷ 7 = 3

Substitute 1 u = 3 into (1).
1 p = 14 - 1 u
1 p = 14 - 1 x 3
1 p = 14 - 3

1 p = 11

Number of stickers that Tim had in the end
= 1 p
= 11

Answer(s): 11