Pierre, Luis and Glen had a total of 112 erasers. The ratio of Luis's erasers to Glen's erasers was 8 : 3 at first. Pierre and Luis each gave away ¹₂ of their erasers. Given that the three boys had 68 erasers left, how many erasers did Pierre have in the end?

	Pierre	Luis	Glen	Total
Comparing Luis and Glen at first		8 u	3 u
Before	2 p	2x4 = 8 u	3 u	112
Change	- 1 p	-1x4 = - 4 u		- 44
After	1 p	1x4 = 4 u	3 u	68

Total number of erasers that Pierre and Luis gave away
= 112 - 68
= 44

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

1 p + 4 u = 112 - 68
1 p + 4 u = 44
1 p = 44 - 4 u --- (1)

1 p + 4 u + 3 u = 68
1 p + 7 u = 68
1 p = 68 - 7 u --- (2)

(1) = (2)
44 - 4 u = 68 - 7 u
7 u - 4 u = 68 - 44
7 u - 4 u = 24
3 u = 24

1 u = 24 ÷ 3 = 8

Substitute 1 u = 8 into (1).
1 p = 44 - 4 u
1 p = 44 - 4 x 8
1 p = 44 - 32

1 p = 12

Number of erasers that Pierre had in the end
= 1 p
= 12

Answer(s): 12