You can probably cut 8 quantity of 5 inch squares across the WOF.
You use 2 squares of background and 2 squares of scraps for each 4 Patch block. Each WOF background cut would make 4 blocks of 4 patches.
For a yard of material, you should get about 7 rows of the 5 inch squares (8 quantity across). This equals 56 quantity of 5 inch squares or 28 blocks of 4 patches.
We don't know the size of quilt. You may want to oversize the quilt if it needs to fit a certain size bed. A queen quilt may shrink about 5-7 inches in the first wash.
PS: Hope all the math and calculations are right or at least a close estimate.