Difficulty: Easy

Average Score: 86%

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) dollars, for the service as a function of the number of times the lawn is mowed, m?

Rationale

A(m) = 5m + 25

This equation accurately represents the total monthly charge, where $5 is the cost per lawn mowed (m) and $25 is a fixed fee. The structure of the equation reflects a linear relationship between the number of lawns mowed and the total charge incurred.

A (A(m) = 5(25)m) YOUR ANSWER

This equation suggests that the charge is calculated by multiplying 5 by 25 and then by m, which would imply a total charge of $125 per lawn mowed. This does not align with the context, as it misrepresents the pricing structure.

B (A(m) = (5 + 25)m) YOUR ANSWER

This equation implies that the total charge is a single rate of $30 per lawn mowed, which is not accurate. It incorrectly combines the fixed fee and the per-lawn charge into one rate instead of separating them.

D (A(m) = 25m + 5) YOUR ANSWER

This equation reverses the coefficients, suggesting a charge of $25 per lawn mowed with a $5 fixed fee. This contradicts the problem's stipulation that the charge per lawn is $5.

E (A(m) = m + 5 + 25) YOUR ANSWER

This equation simplifies to A(m) = m + 30, which implies a charge of $1 per lawn mowed and a total fixed cost of $30. This does not represent the correct pricing model as it fails to account for the specified rates.

Conclusion

The correct function for the total monthly charge, A(m), is represented by the equation A(m) = 5m + 25, accurately reflecting a $5 charge for each lawn mowed plus a $25 fixed service fee. The other options misrepresent the pricing structure through incorrect multipliers or incorrect combination of the per-lawn and fixed fees, leading to inaccurate interpretations of total charges.