Daniel, Perry and Harry had a total of 35 stickers. The ratio of Perry's stickers to Harry's stickers was 2 : 7 at first. Daniel and Perry each gave away ¹₂ of their stickers. Given that the three boys had 28 stickers left, how many stickers did Daniel have in the end?

	Daniel	Perry	Harry	Total
Comparing Perry and Harry at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	35
Change	- 1 p	-1x1 = - 1 u		- 7
After	1 p	1x1 = 1 u	7 u	28

Total number of stickers that Daniel and Perry gave away
= 35 - 28
= 7

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

1 p + 1 u = 35 - 28
1 p + 1 u = 7
1 p = 7 - 1 u --- (1)

1 p + 1 u + 7 u = 28
1 p + 8 u = 28
1 p = 28 - 8 u --- (2)

(1) = (2)
7 - 1 u = 28 - 8 u
8 u - 1 u = 28 - 7
8 u - 1 u = 21
7 u = 21

1 u = 21 ÷ 7 = 3

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

1 p = 4

Number of stickers that Daniel had in the end
= 1 p
= 4

Answer(s): 4