Verified answer

You can start with a simple tune-up. Fresh Oil and oil filter, new spark plugs and wires, new air filter, new fuel filter, flush transmission fluid and put new in.

Start there and see if there is any improvement, if not its probably something more serious.

In 1968 nobody cared about gas mileage. Gas was around $.20/gallon. I doubt if a big heavy Riviera could get better than 8-10 MPG.

Any depended on private mechanic can do a gas pump stress attempt on the gas rail stress installation beside the gas injector nozzles. If the gas stress is below 35 psi., you like a sparkling Delphi or AC-Delco (typical kit) electric powered gas pump. If the motor has a manufacturing facility supercharger the stress spec is 40 psi. A GM broking won't guarantee the different sort of gas pump. in case you like a Bosh electric powered gas pump Robert the non-mechanic will set up and guarantee it.

In some countries where gas prices are even higher than in the US,they swap thirsty gas engines for diesels.

Make sure its tuned up and running properly and keep your foot out of it, soon as you open up the secondary carb barrels you can watch your gas gage drop. the imaginary egg between your foot and accelerator peddle theory was invented for those old boats.

If the tires' inflation is too loo, that's a big drag on mpg, & balance & alignment.

& a tune up.

dont drive over 55; wind resistance increases exponentially over that.

Sell it.