25. Which of the following equations represents the total monthly charge, A (m) dollars, for the service as a function of the number of times the lawn is mowed, m?
Answer: C
A(m) = 5m + 25
The equation that represents the total monthly charge for the lawn care service is A(m) = 5m + 25, where $25 is the flat fee and $5 is charged for each mowing.
A) A(m) = 5(25)m
This option incorrectly suggests a multiplication of the flat fee of $25 by the number of mows, which doesn't accurately reflect the addition of charges. The correct model should add the flat fee to the variable cost based on the number of mows.
B) A(m) = (5 + 25)m
This equation implies that both the flat fee and the per-mow charge are multiplied by the number of mows, which is incorrect. The flat fee should remain a constant addition rather than being multiplied.
C) A(m) = 5m + 25
This option correctly represents the total charge, where $5 is the cost for each mowing (m) and $25 is the fixed monthly fee. Thus, it accurately models the pricing structure provided in the extract.
D) A(m) = 25m + 5
This equation incorrectly positions the flat fee as a variable cost that increases with the number of mows. The flat fee should remain constant at $25, while the variable cost should be $5 per mowing.
E) A(m) = m + 5 + 25
This option misrepresents the cost structure by treating the number of mows as a simple addition rather than a multiplication by the variable charge of $5. It does not accurately reflect the total charge.
Conclusion
The correct equation is A(m) = 5m + 25, which appropriately combines the flat fee with the variable costs based on mows. All other options fail to properly represent the charge structure outlined in the extract, either by misapplying the multiplication or addition rules concerning fixed and variable costs.