Cole, Albert and John had a total of 138 marbles. The ratio of Albert's marbles to John's marbles was 6 : 7 at first. Cole and Albert each gave away ¹₂ of their marbles. Given that the three boys had 104 marbles left, how many marbles did Cole have in the end?

	Cole	Albert	John	Total
Comparing Albert and John at first		6 u	7 u
Before	2 p	2x3 = 6 u	7 u	138
Change	- 1 p	-1x3 = - 3 u		- 34
After	1 p	1x3 = 3 u	7 u	104

Total number of marbles that Cole and Albert gave away
= 138 - 104
= 34

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

1 p + 3 u = 138 - 104
1 p + 3 u = 34
1 p = 34 - 3 u --- (1)

1 p + 3 u + 7 u = 104
1 p + 10 u = 104
1 p = 104 - 10 u --- (2)

(1) = (2)
34 - 3 u = 104 - 10 u
10 u - 3 u = 104 - 34
10 u - 3 u = 70
7 u = 70

1 u = 70 ÷ 7 = 10

Substitute 1 u = 10 into (1).
1 p = 34 - 3 u
1 p = 34 - 3 x 10
1 p = 34 - 30

1 p = 4

Number of marbles that Cole had in the end
= 1 p
= 4

Answer(s): 4