Jeremy, David and Tommy had a total of 92 marbles. The ratio of David's marbles to Tommy's marbles was 4 : 5 at first. Jeremy and David each gave away ¹₂ of their marbles. Given that the three boys had 66 marbles left, how many marbles did Jeremy have at first?

	Jeremy	David	Tommy	Total
Comparing David and Tommy at first		4 u	5 u
Before	2 p	2x2 = 4 u	5 u	92
Change	- 1 p	-1x2 = - 2 u		- 26
After	1 p	1x2 = 2 u	5 u	66

Total number of marbles that Jeremy and David gave away
= 92 - 66
= 26

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

1 p + 2 u = 92 - 66
1 p + 2 u = 26
1 p = 26 - 2 u --- (1)

1 p + 2 u + 5 u = 66
1 p + 7 u = 66
1 p = 66 - 7 u --- (2)

(1) = (2)
26 - 2 u = 66 - 7 u
7 u - 2 u = 66 - 26
7 u - 2 u = 40
5 u = 40

1 u = 40 ÷ 5 = 8

Substitute 1 u = 8 into (1).
1 p = 26 - 2 u
1 p = 26 - 2 x 8
1 p = 26 - 16

1 p = 10

Number of marbles that Jeremy had at first
= 2 p
= 2 x 10
= 20

Answer(s): 20