Pierre, Andy and Henry had a total of 84 stickers. The ratio of Andy's stickers to Henry's stickers was 8 : 7 at first. Pierre and Andy each gave away ¹₂ of their stickers. Given that the three boys had 56 stickers left, how many stickers did Pierre have at first?

	Pierre	Andy	Henry	Total
Comparing Andy and Henry at first		8 u	7 u
Before	2 p	2x4 = 8 u	7 u	84
Change	- 1 p	-1x4 = - 4 u		- 28
After	1 p	1x4 = 4 u	7 u	56

Total number of stickers that Pierre and Andy gave away
= 84 - 56
= 28

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

1 p + 4 u = 84 - 56
1 p + 4 u = 28
1 p = 28 - 4 u --- (1)

1 p + 4 u + 7 u = 56
1 p + 11 u = 56
1 p = 56 - 11 u --- (2)

(1) = (2)
28 - 4 u = 56 - 11 u
11 u - 4 u = 56 - 28
11 u - 4 u = 28
7 u = 28

1 u = 28 ÷ 7 = 4

Substitute 1 u = 4 into (1).
1 p = 28 - 4 u
1 p = 28 - 4 x 4
1 p = 28 - 16

1 p = 12

Number of stickers that Pierre had at first
= 2 p
= 2 x 12
= 24

Answer(s): 24