For an emergency service call, a plumbing company charges a flat fee of $60 plus $40 an hour. A customer remembers paying at least $200 for an emergency service. Which phrase describes the number of hours the plumbing company was at the service call?

Rationale

At least 3.5 hours.

To determine the number of hours for which the plumbing company was called, we can set up the equation based on the total charge. The customer paid at least $200, which includes a flat fee of $60 plus $40 for each hour of service. By solving the inequality, we find the minimum number of hours.

A (at most 2 hours) YOUR ANSWER

If the plumbing service lasted at most 2 hours, the total charge would be $60 + $40 * 2 = $140. This amount is less than $200, making this option incorrect.

B (at most 3.5 hours) YOUR ANSWER

Calculating for at most 3.5 hours results in a total charge of $60 + $40 * 3.5 = $140 + $60 = $200. While this total meets the requirement, it does not account for the phrase "at most," which implies that the service could have been longer. Therefore, it is not the best description of the situation.

C (at least 3.5 hours) CORRECT

When calculating for at least 3.5 hours, the minimum charge would be $60 + $40 * 3.5 = $200. Since the customer remembers paying at least $200, this option accurately describes the situation, indicating that the service must have lasted at least this duration.

D (at least 2 hours) YOUR ANSWER

If the service lasted at least 2 hours, the total charge would be $60 + $40 * 2 = $140. Since this total does not meet the customer's memory of paying at least $200, this choice cannot accurately describe the situation.

Conclusion

The calculation reveals that for a customer who paid at least $200, the plumbing service must have lasted at least 3.5 hours. This is the only option that aligns with both the fee structure and the customer's recollection of the total cost, making it the correct choice. The other options either underestimate the duration or provide inaccurate maximum limits.

For an emergency service call, a plumbing company charges a flat fee of $60 plus $40 an hour. A customer remembers paying at least $200 for an emergency service. Which phrase describes the number of hours the plumbing company was at the service call?

At least 3.5 hours.

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