We are given two phone plans:

• Plan A: A fixed monthly fee of $25, plus $0.11 per minute of calls.
• Plan B: No fixed fee, but it charges $0.16 per minute of calls.

We need to find:

1. The number of minutes when both plans cost the same.
2. The cost when both plans are equal.

Step 1: Set up the cost equations for both plans.

• Let $m$ represent the number of minutes of calling.

For Plan A, the total cost is: $\text{Cost of Plan A} = 25 + 0.11m$ For Plan B, the total cost is: $\text{Cost of Plan B} = 0.16m$

Step 2: Set the two cost equations equal to find when the costs are the same.

$25 + 0.11m = 0.16m$

Step 3: Solve for $m$.

First, subtract $0.11m$ from both sides: $25 = 0.05m$

Now, divide both sides by 0.05: $m = \frac{25}{0.05} = 500$

So, the two plans cost the same after 500 minutes.

Step 4: Find the cost when the two plans are equal.

Substitute $m = 500$ into either equation. Using Plan B's cost equation: $\text{Cost of Plan B} = 0.16 \times 500 = 80$

Thus, the cost when both plans are equal is $80.

Let me know if you need more details or have any other questions!

Follow-up Questions:

1. What if Plan B had a fixed fee too, how would you adjust the equations?
2. What if Plan A charged $0.12 per minute instead of $0.11, how would that affect the solution?
3. How many minutes would make Plan A cheaper than Plan B?
4. If a person talks for 300 minutes, which plan would be cheaper and by how much?
5. How could you graph the cost functions for these two plans to visualize the break-even point?

Tip: Comparing linear costs like these helps find "break-even" points, which can apply to a lot of financial decisions, like choosing between service plans.