A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $7.40 and then an additional 5 cents per minute of use. In Plan B, there is no monthly fee, but the customer pays 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost more than Plan B?
Use m for the number of minutes of phone use in a month, and solve your inequality for m.
 


We are tasked with determining when Plan A costs more than Plan B based on the number of minutes $ m $ used in a month.

### Step 1: Define the cost expressions for each plan.
- **Plan A:** The customer pays a fixed monthly fee of $7.40 plus 5 cents per minute. The total cost for Plan A is:
  \[
  \text{Cost of Plan A} = 7.40 + 0.05m
  \]
- **Plan B:** The customer pays no monthly fee but is charged 7 cents per minute. The total cost for Plan B is:
  \[
  \text{Cost of Plan B} = 0.07m
  \]

### Step 2: Set up the inequality.
We want to find when Plan A costs more than Plan B, so we set up the inequality:
\[
7.40 + 0.05m > 0.07m
\]

### Step 3: Solve the inequality.
First, subtract $ 0.05m $ from both sides to isolate $ m $ on one side:
\[
7.40 > 0.07m - 0.05m
\]
Simplifying the right-hand side:
\[
7.40 > 0.02m
\]

Now, divide both sides by $ 0.02 $ to solve for $ m $:
\[
m < \frac{7.40}{0.02}
\]

Perform the division:
\[
m < 370
\]

### Conclusion:
Plan A will cost more than Plan B when the number of minutes used in a month is less than 370. Therefore, Plan A is more expensive for any usage **less than 370 minutes**.

Would you like further details or have any questions?

Here are 5 related questions you might explore:
1. At how many minutes does Plan A and Plan B cost the same?
2. What is the total cost for 200 minutes of use in Plan A?
3. What is the total cost for 450 minutes of use in Plan B?
4. How much will a user save by switching from Plan A to Plan B if they use 350 minutes?
5. For what number of minutes would both plans exceed $40 in total cost?

**Tip:** When comparing plans with a fixed fee and per-minute charge, setting up inequalities is a useful way to determine the break-even point.

A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $7.40 and then an additional 5 cents per minute of use. In Plan B, there is no monthly fee, but the customer pays 7 cents per minute of use. For what amounts of monthly phone use will Plan A cost more than Plan B? Use m for the number of minutes of phone use in a month, and solve your inequality for m.

Learn how to compare two phone plans using inequalities to determine when Plan A costs more than Plan B. The problem involves basic algebra concepts such as linear equations and inequalities. Suitable for students in Grades 7-9.

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