https://file.aiquickdraw.com/mathbot/file/1729095004169pme3c8hj.jpg

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.

A phone company offers two monthly plans. Plan A costs $25 plus an additional $0.11 for each minute of calls. Plan B has no initial fee but costs $0.16 for each minute of calls. For what amount of calling do the two plans cost the same? What is the cost when the two plans cost the same?

Learn how to compare two phone plans, one with a fixed fee and one without, by solving linear equations. This problem involves finding the break-even point and calculating when the total costs are equal. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation