Zeph, Tom and Reggie had a total of 96 erasers. The ratio of Tom's erasers to Reggie's erasers was 4 : 5 at first. Zeph and Tom each gave away ¹₂ of their erasers. Given that the three boys had 73 erasers left, how many erasers did Zeph have in the end?

	Zeph	Tom	Reggie	Total
Comparing Tom and Reggie at first		4 u	5 u
Before	2 p	2x2 = 4 u	5 u	96
Change	- 1 p	-1x2 = - 2 u		- 23
After	1 p	1x2 = 2 u	5 u	73

Total number of erasers that Zeph and Tom gave away
= 96 - 73
= 23

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

1 p + 2 u = 96 - 73
1 p + 2 u = 23
1 p = 23 - 2 u --- (1)

1 p + 2 u + 5 u = 73
1 p + 7 u = 73
1 p = 73 - 7 u --- (2)

(1) = (2)
23 - 2 u = 73 - 7 u
7 u - 2 u = 73 - 23
7 u - 2 u = 50
5 u = 50

1 u = 50 ÷ 5 = 10

Substitute 1 u = 10 into (1).
1 p = 23 - 2 u
1 p = 23 - 2 x 10
1 p = 23 - 20

1 p = 3

Number of erasers that Zeph had in the end
= 1 p
= 3

Answer(s): 3