Question 31

A(m) = 5m + 25

The total monthly charge, A(m), can be expressed as the sum of a flat fee of $25 and a variable charge of $5 for each time the lawn is mowed, represented as 5m. Thus, the correct equation is A(m) = 5m + 25.

A) A(m) = 5(25)m

This option incorrectly suggests that the total charge is calculated by multiplying 5 by 25 and then by m, which does not correctly represent the flat fee plus the variable charge. The formula lacks the proper structure to account for the constant $25 charge.

B) A(m) = 5 + 25m

This option misrepresents the relationship by placing the variable charge after the flat fee, implying a different calculation method. It suggests that the charge increases by 25 for each mow, rather than maintaining a flat fee of $25.

C) A(m) = 5m + 25

This option accurately reflects the structure of the total charge. It combines the flat fee of $25 with the variable fee of $5 multiplied by the number of times the lawn is mowed, aligning perfectly with the given information.

D) A(m) = 25m + 5

This option incorrectly prioritizes the number of mows (m) by assigning it to the flat fee, suggesting that the charge increases significantly with each mow. It does not reflect the correct addition of a flat fee to the variable charge.

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

This option presents a disorganized equation that adds constant values incorrectly. It does not maintain the necessary structure of a flat fee and a variable fee related to the number of mows.

Conclusion

The equation A(m) = 5m + 25 is definitively correct as it accurately represents the total monthly charge by combining a flat fee with a charge based on the number of mows. All other options fail to correctly structure or prioritize the components of the charge, leading to miscalculations regarding the total cost.