I've worked on systems that solve this problem before. I think the ideal solution is a precomputed column, which gets you the best of both worlds. Your total would be a field somewhere, thus no expensive lookups, but it can't get out of sync with the rest of your data (the database maintains the integrity). I don't remember which RDMSs support precomputed columns, but if you don't have transactions, that might not be available either.
You could potentially fake precomputed columns (very effectively... I see no downside) using triggers. You'd probably need transactions though. IMHO, keeping data integrity when you're doing this sort of controlled denormalization is the only legitimate use for a trigger.
