A plumbing company charges $100 for the first hour, $80 for the second hour, and $50 for each additional hour (t ≥ 3). Which equation represents the cost C(t)?

Rationale

C(t)=180+50(t-2)

The equation accurately reflects the pricing structure of the plumbing company by accounting for the first two hours at their respective rates and applying the additional hourly charge for any time beyond that. Specifically, the total cost starts at $180 for the first two hours, with an additional $50 charged for each hour thereafter.

A (C(t)=180+50(t-2)) CORRECT

This equation correctly represents the cost structure: it sums the first hour's fee of $100 and the second hour's fee of $80, totaling $180. For every hour beyond the second hour (t ≥ 3), it adds $50 for each additional hour, represented by the term 50(t-2).

B (C(t)=100+50(t-2)) YOUR ANSWER

This equation incorrectly starts the total cost with only the first hour's charge of $100. It fails to include the second hour's fee, leading to an inaccurate total cost calculation that does not reflect the company's pricing model.

C (C(t)=180+50t) YOUR ANSWER

While this equation begins correctly with $180, it incorrectly applies the additional charge of $50 multiplied by the total hours (t) rather than just for hours beyond the second hour. This results in an inflated cost for hours already accounted for, misrepresenting the actual pricing structure.

D (C(t)=100+50t) YOUR ANSWER

This equation inaccurately starts with the charge for the first hour only and applies the additional charge of $50 for all hours, completely disregarding the second hour's cost of $80. Thus, it fails to represent the correct total cost based on the company's pricing policy.

Conclusion

The equation C(t)=180+50(t-2) accurately represents the plumbing company's pricing strategy by correctly summing the costs for the first two hours and applying the additional hourly rate for any subsequent hours. The other options either miscalculate the initial costs or improperly apply the additional hourly fee, leading to incorrect total cost representations.

A plumbing company charges $100 for the first hour, $80 for the second hour, and $50 for each additional hour (t ≥ 3). Which equation represents the cost C(t)?

C(t)=180+50(t-2)

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