new alternator, or batter, or both?

I'm about to install my new rockford 351M and my two mclass memphis 12" subwoofers. The amp puts out a 376 RMS (little rockford certificate thingy says) at 14.4, I have a duralast titanium batter, and a brand new alternator, that puts out 110 amps The amp is rated at 376 RMS power, I don't know how to calculate all the amperage, and other figures, so could someone with the knowledge to let me know if I will need another alternator, or battery?? Id really apprciate some expertise on this one, because I really don't want to purchase a new alternator. Or.. Can an isolator and a second battery work for me?? I know the battery is only a factor if listening with the car off, and the alternator when it's on. I just don't want to eat my 6 month old alternator up after just replacing it, or having to get a new one when there can be another alternative. I really appreciate any feedback, thanks.

Another option is to use a 0.5 farad capacitor.  This will store power from the battery and save it for the amp.  Less stress on both the battery and amp.  and as far as how many amps that you are using, most good amps have either a 25 or 30 amp fuse with them.  The amp only uses half of that amperage, so your in good shape.

Well if you were going to replace your battery, it wouldn't be a bad idea to replace your alternator as well. If your battery hasn't been acting up for that long you may not need to replace it. I think Autozone and places like that do a free battery and alternator test for you.~The Rookie~

Rookie of the year that is...

Don't let the smoke out of your equiptment..it doesn't go back in.

Thanks a lot for the help. Nah, I don't listen to the radio with the car off, if I'm listening, I'm moving, or if rarely, when people want to hear it. The battery and the alternator got dropped at the same time, it has 850 cca and 750 ca, and 125 reserve if that makes a difference. The battery and the alternator are just 6 months old, and I hadn't put a system on it, until now, because I sold my old one.