Cut the binding strip you have into about 16 inch lengths, sew two lengths together to get a 3 3/4 inch wide strip. Use another fabric cut 3 3/4 inch wide and alternate the strips, sewing them into the length you need for the binding. You'll have a nice looking binding and no one will ever know you didn't plan it that way.
The way I measure binding width is double how wide I want the binding to be on the quilt and add 1/4 inch. I press it half longways and sew the raw ends to the quilt, turn and hand sew the folded end to the other side. Happy quilting. :-)