Jeremy, Daniel and Glen had a total of 31 marbles. The ratio of Daniel's marbles to Glen's marbles was 2 : 7 at first. Jeremy and Daniel each gave away ¹₂ of their marbles. Given that the three boys had 26 marbles left, how many marbles did Jeremy have in the end?

	Jeremy	Daniel	Glen	Total
Comparing Daniel and Glen at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	31
Change	- 1 p	-1x1 = - 1 u		- 5
After	1 p	1x1 = 1 u	7 u	26

Total number of marbles that Jeremy and Daniel gave away
= 31 - 26
= 5

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

1 p + 1 u = 31 - 26
1 p + 1 u = 5
1 p = 5 - 1 u --- (1)

1 p + 1 u + 7 u = 26
1 p + 8 u = 26
1 p = 26 - 8 u --- (2)

(1) = (2)
5 - 1 u = 26 - 8 u
8 u - 1 u = 26 - 5
8 u - 1 u = 21
7 u = 21

1 u = 21 ÷ 7 = 3

Substitute 1 u = 3 into (1).
1 p = 5 - 1 u
1 p = 5 - 1 x 3
1 p = 5 - 3

1 p = 2

Number of marbles that Jeremy had in the end
= 1 p
= 2

Answer(s): 2