Fabian, Mark and John had a total of 58 marbles. The ratio of Mark's marbles to John's marbles was 6 : 5 at first. Fabian and Mark each gave away ¹₂ of their marbles. Given that the three boys had 39 marbles left, how many marbles did Fabian have at first?

	Fabian	Mark	John	Total
Comparing Mark and John at first		6 u	5 u
Before	2 p	2x3 = 6 u	5 u	58
Change	- 1 p	-1x3 = - 3 u		- 19
After	1 p	1x3 = 3 u	5 u	39

Total number of marbles that Fabian and Mark gave away
= 58 - 39
= 19

The number of marbles that Mark had at first is repeated.  Make the number of marbles that Mark had at first the same.  LCM of 6 and 2 is 6.

1 p + 3 u = 58 - 39
1 p + 3 u = 19
1 p = 19 - 3 u --- (1)

1 p + 3 u + 5 u = 39
1 p + 8 u = 39
1 p = 39 - 8 u --- (2)

(1) = (2)
19 - 3 u = 39 - 8 u
8 u - 3 u = 39 - 19
8 u - 3 u = 20
5 u = 20

1 u = 20 ÷ 5 = 4

Substitute 1 u = 4 into (1).
1 p = 19 - 3 u
1 p = 19 - 3 x 4
1 p = 19 - 12

1 p = 7

Number of marbles that Fabian had at first
= 2 p
= 2 x 7
= 14

Answer(s): 14