Rael, Jeremy and Neave had a total of 93 erasers. The ratio of Jeremy's erasers to Neave's erasers was 4 : 3 at first. Rael and Jeremy each gave away ¹₂ of their erasers. Given that the three boys had 63 erasers left, how many erasers did Rael have at first?

	Rael	Jeremy	Neave	Total
Comparing Jeremy and Neave at first		4 u	3 u
Before	2 p	2x2 = 4 u	3 u	93
Change	- 1 p	-1x2 = - 2 u		- 30
After	1 p	1x2 = 2 u	3 u	63

Total number of erasers that Rael and Jeremy gave away
= 93 - 63
= 30

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

1 p + 2 u = 93 - 63
1 p + 2 u = 30
1 p = 30 - 2 u --- (1)

1 p + 2 u + 3 u = 63
1 p + 5 u = 63
1 p = 63 - 5 u --- (2)

(1) = (2)
30 - 2 u = 63 - 5 u
5 u - 2 u = 63 - 30
5 u - 2 u = 33
3 u = 33

1 u = 33 ÷ 3 = 11

Substitute 1 u = 11 into (1).
1 p = 30 - 2 u
1 p = 30 - 2 x 11
1 p = 30 - 22

1 p = 8

Number of erasers that Rael had at first
= 2 p
= 2 x 8
= 16

Answer(s): 16