Global Telephone charges 30 dollars for monthly phone service, plus a long distance calling rate of 15 cents per minute. After an hour of long distance calling charges,the rate drops to just 5 cents per minute for additional long distance calls.
What will the monthly bill be if you make 150 minutes of long distance calls?
If the phone bill was 45 dollars, how many minutes of long distance calls did you make?
Let n denote the number of minutes of long distance service you use in a given month. Find a formula involving n that expresses your monthly telephone bill.
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To calculate the monthly bill for long distance calls, we need to consider the flat fee for monthly phone service, the per-minute charge for the initial hour of long distance calls, and the reduced per-minute charge for any additional long distance calls.
1. To find the monthly bill if you make 150 minutes of long distance calls:
- The flat fee for monthly phone service is $30.
- For the first hour of long distance calls, the rate is 15 cents per minute. So, for 60 minutes, the cost would be 60 * $0.15 = $9.
- After the first hour, the rate drops to 5 cents per minute. Therefore, for the remaining 90 minutes (150 - 60), the cost would be 90 * $0.05 = $4.50.
- Adding up the flat fee and the charges for long distance calls, the monthly bill would be $30 + $9 + $4.50 = $43.50.
2. To determine the number of minutes of long distance calls if the phone bill is $45:
- Subtract the flat fee for monthly phone service ($30) from the total bill: $45 - $30 = $15.
- For the first hour of long distance calls, the rate is 15 cents per minute. So, the number of minutes for this part would be $15 / $0.15 = 100 minutes.
- The remaining $15 is the cost for additional long distance calls at the reduced rate of 5 cents per minute. Therefore, the number of minutes for this part would be $15 / $0.05 = 300 minutes.
- Adding up the minutes for both parts, the total number of minutes of long distance calls would be 100 + 300 = 400 minutes.
3. To find a formula involving n that expresses the monthly telephone bill:
- Let n be the number of minutes of long distance service used in a given month.
- The flat fee for monthly phone service is $30.
- For the first hour of long distance calls, the cost would be n * $0.15.
- After the first hour, the cost for additional long distance calls would be (n - 60) * $0.05.
- Therefore, the formula for the monthly telephone bill would be: Bill = $30 + n * $0.15 (for n ≤ 60), Bill = $30 + (60 * $0.15) + (n - 60) * $0.05 (for n > 60).