A landscaping company mows x properties per month for m months. For each property, landscape maintenance starts at c dollars. If the company charges y dollars per square yard and the average lawn area per property is z square yards, which of the following expressions represents the monthly revenue of the landscaping company?
Axyz + c
(yz + c)x
(yz + c)mx
(xyz + c)m
The correct answer and explanation is:
The correct expression for the monthly revenue of the landscaping company is (yz + c) x.
Explanation:
- Revenue from maintenance: The maintenance for each property starts at c dollars. This is a fixed cost for each property, regardless of the lawn size.
- Revenue from lawn area: The company also charges y dollars per square yard for the area of the lawn. Given that the average lawn area per property is z square yards, the revenue from each property’s lawn area is y * z dollars.
- Total revenue per property: For each property, the total revenue is the sum of the maintenance cost c and the lawn area revenue y * z. Thus, the total revenue for one property is yz + c.
- Total revenue for x properties per month: If the company mows x properties per month, the total monthly revenue from mowing all properties is (yz + c) * x.
- Revenue over m months: Since the company works for m months, the total revenue over all m months would be (yz + c) * x * m. But for monthly revenue, you would focus on the revenue per month, which is (yz + c) * x.
Hence, (yz + c) x is the correct expression representing the company’s monthly revenue. This is the sum of the fixed maintenance charge and the variable charge based on the lawn area, multiplied by the number of properties mowed each month.