You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $25.00 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $15.00 with a charge of $0.15 per minute for all long-distance calls. Complete parts a and b.
a. For how many minutes of long-distance calls will the costs for the two plans be the same?
To find the number of minutes where the costs for the two plans are the same, we need to set up an equation.
For Plan A, the cost is $25 + $0.05 per minute.
For Plan B, the cost is $15 + $0.15 per minute.
Let's set these two expressions equal to each other and solve for the number of minutes (m) when the costs are the same:
$25 + $0.05m = $15 + $0.15m
Subtracting $0.05m from both sides gives:
$10 = $0.1m
Dividing both sides by $0.1 gives:
m = $10 / $0.1 = 100
Therefore, for 100 minutes of long-distance calls, the costs for Plan A and Plan B will be the same.
b. Which plan is better if you expect to use less than 100 minutes?
What will be the cost for each plan?
To determine the cost for each plan, we need to calculate the total cost based on the number of minutes of long-distance calls.
For Plan A, the cost is $25.00 plus $0.05 per minute.
For Plan B, the cost is $15.00 plus $0.15 per minute.
Let's calculate the costs for each plan for various numbers of minutes:
For Plan A:
1. 10 minutes: $25.00 + ($0.05 * 10) = $25.00 + $0.50 = $25.50
2. 50 minutes: $25.00 + ($0.05 * 50) = $25.00 + $2.50 = $27.50
3. 100 minutes: $25.00 + ($0.05 * 100) = $25.00 + $5.00 = $30.00
4. 150 minutes: $25.00 + ($0.05 * 150) = $25.00 + $7.50 = $32.50
For Plan B:
1. 10 minutes: $15.00 + ($0.15 * 10) = $15.00 + $1.50 = $16.50
2. 50 minutes: $15.00 + ($0.15 * 50) = $15.00 + $7.50 = $22.50
3. 100 minutes: $15.00 + ($0.15 * 100) = $15.00 + $15.00 = $30.00
4. 150 minutes: $15.00 + ($0.15 * 150) = $15.00 + $22.50 = $37.50
Therefore, the cost for each plan for various numbers of minutes would be as follows:
Plan A:
- 10 minutes: $25.50
- 50 minutes: $27.50
- 100 minutes: $30.00
- 150 minutes: $32.50
Plan B:
- 10 minutes: $16.50
- 50 minutes: $22.50
- 100 minutes: $30.00
- 150 minutes: $37.50
In this comparison, Plan B is better if you expect to use less than 100 minutes as it has a lower base monthly fee ($15.00) compared to Plan A ($25.00). However, for usage exceeding 100 minutes, Plan A becomes more cost-effective.