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Noah is having his driveway resurfaced, which costs per square meter. The driveway will also be given new edging around its perimeter, which costs per meter. Let be the area, in square meters, of the driveway; and let be the total cost of resurfacing the driveway and installing the new edging. If the perimeter of the driveway is meters, which of the following equations correctly relates and ?Choose answer:(A) (B) (C) (D)
Full solution
Q. Noah is having his driveway resurfaced, which costs per square meter. The driveway will also be given new edging around its perimeter, which costs per meter. Let be the area, in square meters, of the driveway; and let be the total cost of resurfacing the driveway and installing the new edging. If the perimeter of the driveway is meters, which of the following equations correctly relates and ?Choose answer:(A) (B) (C) (D)
- Expressing total cost in terms of area: To find the correct equation, we need to express the total cost in terms of the area and the given costs for resurfacing and edging. The cost of resurfacing is per square meter, so the resurfacing cost is .
- Calculating cost of edging: The cost of the edging is per meter, and the perimeter is meters. So, the total cost for the edging is .
- Calculating total cost for edging: Calculate the total cost for the edging: .
- Calculating total cost: Now, add the cost of resurfacing and the cost of edging to get the total cost . The total cost is the sum of the resurfacing cost and the edging cost ().
- Writing the equation for total cost: Write the equation that relates the total cost to the area : .
