How much depends on what is there. What is the level of organic matter in your soil now? These simple tests may help determine that,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2. Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
You want around 5 to 8 percent organic matter in your soil. That can be compost or other types of organic matter, vegetative waste.

Depends on how heavily you wish to apply the compost. A 20'x10' planting area is 200 sq feet.

A 2 inch layer of compost (best as a mulch or topdressing) will require 32 cubic feet, 4 inches will take 66 cubic feet, 6 inches 100 cubic feet and 8 inches 132 cubic feet. 6-8 inches are typically recommended for tilling or amending new planting areas.

A couple of math points to help you with your calculations: 7 gallons is just under 1 cubic foot, so even if applying a very small quantity, you are going to need a LOT of bags. It would be very worthwhile economically to look for bulk compost rather than bagged goods -- it is far less expensive to buy in bulk. This is typically sold by the cubic yard. And there are 27 cubic feet in a cubic yard, so the conversions would be as follows

2" depth = 1.25 cubic yards (approx)
4" depth = 2.5 cubic yards (approx)
6" depth = 4 cubic yards (approx)
8" depth = 5 cubic yards (approx)

(The approximations round up - it is generally better to err on the upside rather than the downside and bulk dealers tend to sell in even parts of a yard)

What is growing in the area now?

I'd go with a cubic yard this spring, and plan to add a bunch of shredded leaves/grass mix tilled into the soil in the fall after harvest and mulch with some more. Anything you add this spring likely won't have a huge affect this growing season, some, but not huge.

I'd deliver a CY of 'post to your driveway for $45 if you were within a few miles of me, more $$ if I had to drive further.

Lloyd

P.S. Not a gardener but that's what I'd do.