Ivan, Riordan and Archie had a total of 96 stickers. The ratio of Riordan's stickers to Archie's stickers was 4 : 7 at first. Ivan and Riordan each gave away ¹₂ of their stickers. Given that the three boys had 76 stickers left, how many stickers did Ivan have in the end?

	Ivan	Riordan	Archie	Total
Comparing Riordan and Archie at first		4 u	7 u
Before	2 p	2x2 = 4 u	7 u	96
Change	- 1 p	-1x2 = - 2 u		- 20
After	1 p	1x2 = 2 u	7 u	76

Total number of stickers that Ivan and Riordan gave away
= 96 - 76
= 20

The number of stickers that Riordan had at first is repeated.  Make the number of stickers that Riordan had at first the same.  LCM of 4 and 2 is 4.

1 p + 2 u = 96 - 76
1 p + 2 u = 20
1 p = 20 - 2 u --- (1)

1 p + 2 u + 7 u = 76
1 p + 9 u = 76
1 p = 76 - 9 u --- (2)

(1) = (2)
20 - 2 u = 76 - 9 u
9 u - 2 u = 76 - 20
9 u - 2 u = 56
7 u = 56

1 u = 56 ÷ 7 = 8

Substitute 1 u = 8 into (1).
1 p = 20 - 2 u
1 p = 20 - 2 x 8
1 p = 20 - 16

1 p = 4

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

Answer(s): 4