A farmer owns a rectangular field that has an area of 2400 square metres. Along one edge of the field is a straight river that is 64 metres long. The farmer wishes to replace the fences that border his adjoining neighbors’ properties. How much will it cost the farmer to replace these fences if a fence costs $5.45 per metre?

Step 1: Identify the dimensions of the rectangle. We know that the area of a rectangle is given by the formula length x width. We know the area is 2400 square meters and one side (the one along the river) is 64 meters. So, the other side can be found by dividing the area by the known side: 2400 / 64 = 37.5 meters.

Step 2: Determine the total length of the fence. The farmer wants to replace the fences that border his neighbors' properties, which means he needs to replace the fences on three sides of the rectangle (the fourth side is the river). So, the total length of the fence is 64 (one long side) + 37.5 (one short side) + 37.5 (the other short side) = 139 meters.

Step 3: Calculate the cost of the fence. We know that the fence costs $5.45 per meter. So, the total cost is 139 (total length of the fence) x 5.45 (cost per meter) =$757.55.

So, it will cost the farmer $757.55 to replace these fences.