Each month, the charge for a lawn care service consists of a flat fee of $25, plus $5 each time the lawn is mowed. Which of the following equations represents the total monthly charge, A(m), in dollars, as a function of the number of × the lawn is mowed, m?
A(m) = 5m + 25
The total monthly charge, A(m), includes a flat fee of $25 plus an additional $5 for each time the lawn is mowed, represented by the variable m. Therefore, the equation correctly combines these components to reflect the total cost.
This choice incorrectly suggests that the total charge is calculated by multiplying the flat fee of $25 by the number of mowings, which does not account for the flat fee being a separate fixed amount. The equation misrepresents the structure of the cost.
This option misplaces the flat fee and the variable cost. It implies that mowing the lawn incurs a cost of $25 for each mowing plus a one-time charge of $5, which is not how the charges are structured. The flat fee should remain as a constant amount added to the total.
In this equation, the flat fee is incorrectly treated as a variable cost dependent on the number of mowings, which is not accurate. The flat fee should be a fixed amount that is independent of the number of times the lawn is mowed.
This choice suggests that the total charge is calculated by adding the number of mowings directly to the costs, which misrepresents the structure of the equation. It does not provide a proper multiplication for the charge per mowing and improperly adds variables in a way that does not reflect the real cost.
The total monthly charge for the lawn care service can be effectively represented by the equation A(m) = 5m + 25, where $25 is the fixed flat fee and $5 is the variable cost for each mowing. This equation accurately captures both components of the charge structure, ensuring a correct representation of total costs based on the number of mowings.
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