You are a representative for a cell phone company and it is your job to promote different cell phone plans. Your boss asks you to visually display two plans and compare them so you can point out the advantages of each plan to your customers.
-Plan A costs a basic fee of $30 per month and 10 cents per text message
-Plan B costs a basic fee of $50 per month and 5 cents per text
1. What are the variables in the problem and the equations for Plan A and Plan B?
2. When are Plan A and Plan B the same price based on the number of texts sent? Explain how you determined this.
3. Determine when Plan A is a better plan to go with (based on the number of texts someone sends). Explain how you determined this.
4. Determine when Plan B is a better plan to go with (based on the number of texts someone sends). Explain how you determined this.
5. If you generally send 100 tests a month, what is the better plan for you? Explain how you determined this.
I would so greatly appreciate any help with this.
A = 30 + 0.10m
B = 50 + 0.05m
see what you can do with those equations.
1. The variables in this problem are:
- N = number of text messages sent.
- C(A) = cost of Plan A.
- C(B) = cost of Plan B.
The equations for Plan A and Plan B are as follows:
- C(A) = $30 (basic fee) + $0.10 (cost per text) * N
- C(B) = $50 (basic fee) + $0.05 (cost per text) * N
2. To find when Plan A and Plan B are the same price, we need to set their costs equal to each other and solve for N:
$30 + $0.10N = $50 + $0.05N
Simplifying the equation:
$0.10N - $0.05N = $50 - $30
$0.05N = $20
N = $20 / $0.05
By dividing both sides by $0.05, we find that when N = 400, Plan A and Plan B will have the same cost.
3. To determine when Plan A is a better plan to go with, you need to compare the costs of Plan A and Plan B for different values of N. If the cost of Plan A is less than the cost of Plan B, then Plan A is better.
For example, let's compare the costs of Plan A and Plan B for N = 100:
C(A) = $30 + $0.10 * 100 = $30 + $10 = $40
C(B) = $50 + $0.05 * 100 = $50 + $5 = $55
Since $40 is less than $55, Plan A is a better option for someone who sends 100 text messages.
4. To determine when Plan B is a better plan to go with, you need to compare the costs of Plan A and Plan B for different values of N. If the cost of Plan B is less than the cost of Plan A, then Plan B is better.
For example, let's compare the costs of Plan A and Plan B for N = 200:
C(A) = $30 + $0.10 * 200 = $30 + $20 = $50
C(B) = $50 + $0.05 * 200 = $50 + $10 = $60
Since $60 is less than $50, Plan B is a better option for someone who sends 200 text messages.
5. If you generally send 100 tests a month, we can evaluate the costs of both plans for N = 100 and determine the better plan:
C(A) = $30 + $0.10 * 100 = $30 + $10 = $40
C(B) = $50 + $0.05 * 100 = $50 + $5 = $55
Since $40 is less than $55, Plan A is the better plan for someone who sends 100 text messages per month.