Question 702255
You have that right idea, but stalled out after Bill.
Let A = Allen's marbles.
Then
(1) B = A + 8 and
(2) C = 2*B or
(3) C = 2*(A + 8) or
(4) C = 2*A + 16 and
(5) D = 3*C or
(6) D = 3*(2*A + 16) or
(7) D = 6*A + 48
Now add 
(8) A + (A + 8) + (2*A + 16) + (6*A + 48) = 92 or
(9) 10*A = 92 -8 -16 -48 or
(10) 10*A = 92 - 72 or
(11) A = 2
Then 
(12) B = 10
(13) C = 20
and
(14) D = 60
Is(2 + 10 + 20 + 60 = 92)?
Is (92 = 92)? Yes 
Answer: Allen has 2 marbles, Bill has 10, Charles has 20 and Daryl has 60.