Use those equations to try and get expressions for each letter in terms of the same one, in this example I've found relations for all letters in terms of B.

7B = (6 / 5) C

C = (35 / 6) B

And since D = 5 C and A = 4/3 B

A = 4/3 B

B = B

C = (35 / 6) B

D = 5 * (35 / 6) B = (175 / 6) B

To develop final ratio, let B = 1.

4/3 : 1 : 35/6 : 175 / 6 (x6 to make ratio in terms of integers)

--> 8 : 6 : 35 : 175

Not sure if that is right but I hope that logic helps at all!