Which equation represents the total cost c of a service contract with a one-time activation cost of $35 and a monthly cost of $23 for t months?

• A. c = 23t + 30
• B. c = 23t + 35
• C. c = 35t + 23
• D. c = 23(t + 35)

Answer: (B)

Total cost is the sum of a one-time activation fee and the ongoing monthly fee for a certain number of months. With a 35-dollar activation and a 23-dollar monthly charge for t months, you multiply the monthly amount by the months and add the activation fee: c = 23t + 35. Because addition can be reordered, c = 23t + 35 is the same as c = 35 + 23t. This form correctly reflects a fixed upfront cost plus a variable cost that scales with time.

The other expressions misrepresent how costs accumulate: using 30 instead of 35 changes the fixed amount; using 35t would imply the activation fee scales with time; and 23(t + 35) would multiply the monthly cost by (t + 35), treating the activation as if it were paid every month or adding an incorrect combined term. Thus, the correct model is c = 23t + 35.