Special air-cooled venting

Sooo...

I got an air cooled hood and a tent for flowering.
Cool...
But...
The air cooled hood plus the 6" duct fan comes out to 30" in width.
Not bad, but it exceeded my expectations by about 4"
This leaves me with an inch on each side with the new tent.

That being said, with a 32"x32" tent, I wonder if I can simply use my 8" inline fan to cool the whole tent while the 6" booster can just run air through the hood?
I would have went with the 36"x36" but it was a 40$ difference and I was just excited to get another "stage" tent, now finances are limited again.

My biggest question is, will the 6" booster do any justice while the 8" inline is at play?
Or should I remove the glass and rely on the 8"?...

Not sure if I understand completely but why not duct the inlet to the lights to pull external air Using the 6” exhausted out. And use the 8” for cooling.

Duct boosters are not worth using. Not designed to move air through long lengths of duct or overcome resistance on their own.
But yeah with an 8" fan venting a small tent you should not need an air cooled hood at all. So you could remove the glass and use it as a standard hood.
You need to make sure all hot air leaves the grow space and house or the whole idea is a waste of time.

I have no room to attach ducting at all to the air cooled hood as the tent is actually measured at 31"x31" when I tried to duct with the 6" out the ducting collapsed. When I tried to exhaust the hood into the room and use the 8" to exhaust the tent, the intake and exhaust of the hood actually got sealed under the negative pressure from the inline fan burning up the duct booster.

The duct booster worked wonders for simple no ducting exhaust of the air cooled hood.

I'm currently just relying on the Inline fan exhausting the tent with a clip on fan moving air around the hood with the glass cover removed.. I unfortunately have to keep the lights about 4" further but I've managed. The 8" is pretty damn powerful, It keeps the tent almost too cold in areas not under direct light. I'm probably just going to move up to a 36"x36" tent and get a 400w wing reflector for the 31x31" and probably a 6" inline or 8" with a variable speed adjuster.

Thank you all though.