To solve the problem, we need to understand what each component of the expression [tex]\(660n + 100\)[/tex] represents.
1. Subscription Fee: This is a one-time cost of [tex]$100.
2. Monthly Costs per Line:
- Unlimited Data Cost: $[/tex]40 per line per month.
- Unlimited Call Cost: [tex]$10 per line per month.
- Unlimited Text Message Cost: $[/tex]10 per line per month.
Therefore, the total monthly cost per line for the data, calls, and texts combined is:
[tex]\[
40 + 10 + 10 = 60 \text{ dollars per line per month}
\][/tex]
3. Cost of Phone: This is a one-time cost of [tex]$300 per line.
Next, let’s calculate the total cost for one line for 6 months:
- Monthly cost for data, calls, and texts for 6 months:
\[
60 \text{ dollars per month} \times 6 \text{ months} = 360 \text{ dollars}
\]
- Adding the one-time phone cost:
\[
360 \text{ dollars} + 300 \text{ dollars} = 660 \text{ dollars}
\]
Thus, the total cost for one line for 6 months is $[/tex]660.
Therefore, when we multiply this total cost by the number of lines [tex]\(n\)[/tex], the expression [tex]\(660n\)[/tex] represents the total cost for [tex]\(n\)[/tex] lines over 6 months, including the data, calls, texts, and the phone. The one-time subscription fee of $100 is added as a fixed cost.
So, the coefficient [tex]\(660\)[/tex] in the expression [tex]\(660n + 100\)[/tex] represents the total cost per line for unlimited data, calls, text messages, and one phone for 6 months.
Hence, the statement which best describes the coefficient [tex]\(660\)[/tex] of [tex]\(n\)[/tex] is:
D. It is the total cost per line for unlimited data, calls, text messages, and one phone for 6 months.
