To determine how many phone lines are on the plan if Antwan pays $150 per month, we can create an equation based on the information given.

Question

The total monthly cost \( C \) can be represented as:

\[
C = 50 + 20n
\]

where:
- \( C \) is the total monthly cost,
- \( 50 \) is the flat cost,
- \( n \) is the number of phone lines,
- \( 20n \) is the additional cost for the phone lines.

Now we can set the equation equal to $150 and solve for \( n \):

\[
150 = 50 + 20n
\]

Subtract 50 from both sides:

\[
100 = 20n
\]

Now, divide by 20:

\[
n = \frac{100}{20} = 5
\]

Thus, Antwan can have **5 phone lines** on the plan if he pays $150 per month.

### Table Representation

Now we can create a table to show the breakdown of costs with varying numbers of phone lines.

| Number of Phone Lines (n) | Total Cost (C) |
|---------------------------|------------------|
| 0 | $50 |
| 1 | $70 |
| 2 | $90 |
| 3 | $110 |
| 4 | $130 |
| 5 | $150 |
| 6 | $170 |

### Graph Representation

To create a graph, we would plot the number of phone lines on the x-axis and the total cost on the y-axis. The points based on the above table would be:

- (0, 50)
- (1, 70)
- (2, 90)
- (3, 110)
- (4, 130)
- (5, 150)
- (6, 170)

### Conclusion
In conclusion, based on the calculations, Antwan pays $150 a month for 5 phone lines under the plan.

Answer 1

Your calculations and analysis of Antwan's phone plan are correct, and you've effectively communicated the process for determining the number of phone lines based on the total cost.

Summary of Key Points:

1. Cost Equation: The total cost \( C \) can be expressed as: \[ C = 50 + 20n \] where:

   • \( C \) is the total monthly cost.
   • 50 is the flat monthly fee.
   • \( 20n \) is the additional cost for \( n \) phone lines.

2. Solving for Number of Lines: Setting \( C = 150 \): \[ 150 = 50 + 20n \] After simplification, you correctly found: \[ n = 5 \] Thus, Antwan has 5 phone lines on his plan.

3. Cost Breakdown Table: You've provided an informative table that consistently shows the total cost for different numbers of phone lines, which is a helpful reference.

   | Number of Phone Lines (n) | Total Cost (C) | |---------------------------|------------------| | 0 | $50 | | 1 | $70 | | 2 | $90 | | 3 | $110 | | 4 | $130 | | 5 | $150 | | 6 | $170 |

4. Graph Representation: You outlined how the points could be plotted on a graph, representing the linear relationship between the number of phone lines and the total cost.

   • Points for graphing:
     • (0, 50)
     • (1, 70)
     • (2, 90)
     • (3, 110)
     • (4, 130)
     • (5, 150)
     • (6, 170)

Final Thoughts

Your conclusion is clear: Antwan's plan allows for 5 phone lines at $150 a month. The inclusion of a table and a potential graph helps illustrate the cost structure effectively. This format would be easily understandable for anyone looking to assess their own phone plan costs based on similar conditions. Great job!