Flynn, Cole and Andy had a total of 142 erasers. The ratio of Cole's erasers to Andy's erasers was 4 : 9 at first. Flynn and Cole each gave away ¹₂ of their erasers. Given that the three boys had 116 erasers left, how many erasers did Flynn have in the end?

	Flynn	Cole	Andy	Total
Comparing Cole and Andy at first		4 u	9 u
Before	2 p	2x2 = 4 u	9 u	142
Change	- 1 p	-1x2 = - 2 u		- 26
After	1 p	1x2 = 2 u	9 u	116

Total number of erasers that Flynn and Cole gave away
= 142 - 116
= 26

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

1 p + 2 u = 142 - 116
1 p + 2 u = 26
1 p = 26 - 2 u --- (1)

1 p + 2 u + 9 u = 116
1 p + 11 u = 116
1 p = 116 - 11 u --- (2)

(1) = (2)
26 - 2 u = 116 - 11 u
11 u - 2 u = 116 - 26
11 u - 2 u = 90
9 u = 90

1 u = 90 ÷ 9 = 10

Substitute 1 u = 10 into (1).
1 p = 26 - 2 u
1 p = 26 - 2 x 10
1 p = 26 - 20

1 p = 6

Number of erasers that Flynn had in the end
= 1 p
= 6

Answer(s): 6