Peter, Brandon and Fabian had a total of 113 erasers. The ratio of Brandon's erasers to Fabian's erasers was 2 : 7 at first. Peter and Brandon each gave away ¹₂ of their erasers. Given that the three boys had 95 erasers left, how many erasers did Peter have in the end?

	Peter	Brandon	Fabian	Total
Comparing Brandon and Fabian at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	113
Change	- 1 p	-1x1 = - 1 u		- 18
After	1 p	1x1 = 1 u	7 u	95

Total number of erasers that Peter and Brandon gave away
= 113 - 95
= 18

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

1 p + 1 u = 113 - 95
1 p + 1 u = 18
1 p = 18 - 1 u --- (1)

1 p + 1 u + 7 u = 95
1 p + 8 u = 95
1 p = 95 - 8 u --- (2)

(1) = (2)
18 - 1 u = 95 - 8 u
8 u - 1 u = 95 - 18
8 u - 1 u = 77
7 u = 77

1 u = 77 ÷ 7 = 11

Substitute 1 u = 11 into (1).
1 p = 18 - 1 u
1 p = 18 - 1 x 11
1 p = 18 - 11

1 p = 7

Number of erasers that Peter had in the end
= 1 p
= 7

Answer(s): 7