It can be hard to compare the lowest daily rate when looking at the total length of a
rental. You mentioned when you checked, a "weekly rate under $300 but total cost of 10 days over $500!"
That would put your weekly rate at $42.86 per day and your 10 day rate at $50 a day.... not much difference in the daily rate, but the total for 10 days sure seems higher ( keeping in mind that all the taxes and fees are spread over 10 days as well). I'm not sure what coupon book mentioned a 10 day rate, so I'm sorry I can't address that issue for you.
The general rule of thumb for a lowest daily rate is for weekend rentals. The most you can stretch a weekend rental is 5 days, if you pick up on a Thursday afternoon and return on a Monday late afternoon or evening.
I decided to check this using Travelocity to compare multiple companies easily.
I didn't know your dates, times and location preference, so I made it up... keep this in mind, as pricing and availability are dependant on these factors and can change from minute to minute!!
(I also recommend checking the individual car rental company websites, after you've narrowed down your search)
I checked: (using a compact car for each search)
full 10 days -- August 5-15(Denver Airport) 12 noon pick up and return
7 days -- Aug 5-12 (Denver Airport) 12 noon pick up and return
5 days (weekday) -- Aug 5-10 (Denver Airport) 12 noon pick up and return
5 days (weekend) -- Thu-Mon (Denver Airport) 12 noon pick up and 6pm return
(links open new windows)The best pricing for the full 10 days was through Thrifty or Dollar
Bottom line... according to my check, your lowest daily rate, and your lowest total rate, is for a 5 day weekend rental (Thursday morning through Monday evening).