It took 2 pallets of grass to cover each of the two areas, and so 4 pallets at 450 square feet per pallet means we have 1800 square feet of grass. In the back. To cover that we tried to get 3 cubic yards of compost. Actually we got the same professional mix that we used as dirt; it's 50% compost. I figure the extra 50% can help to compensate some for the settling that we have seen.
This took 2 trips to Whittlesey Landscape in Round Rock (plus another 2 trips for mulch). The two dirt trips cost $82.49 each (1.5 yards plus 6 bags of mulch to hold the tarp down on it), and then another $119.91 for 54 bags of mulch. A total of $284.89, and one day of driving back and forth, loading and unloading. (Friday).
The next day, Saturday, was distributing the dirt around to the back yard and spreading it. By 5 PM it was starting to drizzle, so now it's mud, but it is supposed to rain for the next two days, and that will help it settle down in around the grass roots (we hope).
It may be a bit too thick; it's hard to tell since it's so light weight.
As you can see, we didn't have enough to completely cover the lawn (I guess we needed 4 cubic yards, or to put it on thinner.)