When I got out of engineering college in 1978, I worked the next three years designing audio gear for Boeing. The lead engineer I worked for was like me, building hi fi equipment at home. He subscribed to "DB" magazine, and I read his copy.
I started college with a slide rule and finished with a TI-51 calculator.
Part of the reason they worked in DB was because they did not have calculators.
Part of my job was to go through and modify all the ARINC specification [That controlled all planes, not just Boeing] to modernize the DB of amplitude and the output impedance of audio side tones. That is a boring task, but after a while, I was really ready to argue with anybody from any company about DB.
If you have a 15.8 to one attenuator and put in series with a 31.6 to one attenuator, then to calculate the attenuation, multiply those two numbers.
If you don't have a calculator, but you know those are 24 db and a 30 db attenuator, you simply add the numbers.
Together they are a 54 db attenuator.... That is 501 to one attenuation.
And don't let anyone confuse you about power DB vs Sound pressure level DB.
If you stay in the same system, a DB is a DB is DB.
The power DB is 10 log base 10 of the ratio.
The SPL DB is 20 log base 10 of the ratio
Power already has a squared term in there, so a square in the ratio amounts to a 2 in front of the log operation. That is explained in here:
http://en.wikipedia.org/wiki/Decibel
http://en.wikipedia.org/wiki/Sound_pressure
Adding the two attenuations depends on them being in series. If the ear plugs are really inside the ear muffs it works.
But if the ear plugs were to be touching the ear muffs, then we would be getting some extra coupling and loosing some attenuation.