You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $50 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $10 with a charge of $0.10 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? ____ minutes
To find the number of minutes where the costs for the two plans are the same, we can set up the following equation:
50 + 0.05x = 10 + 0.10x
Where x represents the number of minutes of long-distance calls.
Simplifying the equation, we have:
40 = 0.05x
Dividing both sides by 0.05, we get:
x = 800
Therefore, the costs for the two plans will be the same after 800 minutes of long-distance calls.
What will be the cost for each plan?
For Plan A, the cost consists of a $50 monthly fee plus a charge of $0.05 per minute for long-distance calls.
For Plan B, the cost consists of a $10 monthly fee plus a charge of $0.10 per minute for long-distance calls.
Let's find the cost for each plan based on various amounts of long-distance calls:
For Plan A:
- 0 minutes: $50
- 100 minutes: $50 + (0.05 * 100) = $55
- 500 minutes: $50 + (0.05 * 500) = $75
- 1000 minutes: $50 + (0.05 * 1000) = $100
For Plan B:
- 0 minutes: $10
- 100 minutes: $10 + (0.10 * 100) = $20
- 500 minutes: $10 + (0.10 * 500) = $60
- 1000 minutes: $10 + (0.10 * 1000) = $110
So, the cost for each plan would be as follows:
- Plan A: $50 per month plus $0.05 per minute for long-distance calls
- Plan B: $10 per month plus $0.10 per minute for long-distance calls