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A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $12 and then an additional 5 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 finding the number of minutes of phone use, denoted by $ m $, for which Plan A costs more than Plan B.

### Plan A:
- No monthly fee.
- 8 cents (or $0.08) per minute.

Thus, the cost of Plan A for $ m $ minutes is:
\[
\text{Cost of Plan A} = 0.08m
\]

### Plan B:
- Monthly fee of $12.
- 5 cents (or $0.05) per minute.

Thus, the cost of Plan B for $ m $ minutes is:
\[
\text{Cost of Plan B} = 12 + 0.05m
\]

### Inequality setup:
We want to find when Plan A costs more than Plan B, so we set up the inequality:
\[
0.08m > 12 + 0.05m
\]

### Solving the inequality:
1. Subtract $ 0.05m $ from both sides:
\[
0.08m - 0.05m > 12
\]
\[
0.03m > 12
\]

2. Divide both sides by 0.03:
\[
m > \frac{12}{0.03}
\]
\[
m > 400
\]

### Conclusion:
Plan A will cost more than Plan B if the customer uses more than **400 minutes** in a month.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore:
1. How much does each plan cost for exactly 400 minutes?
2. What is the cost of Plan A for 500 minutes?
3. At how many minutes will Plan A and Plan B cost the same?
4. If Plan B reduced its monthly fee, at what fee would the plans cost the same at 350 minutes?
5. How does a change in the price per minute for Plan A affect the break-even point?

**Tip:** When comparing two pricing plans, setting up an equation or inequality helps identify break-even points or ranges where one plan becomes more economical than the other.

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $12 and then an additional 5 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.

Find out how to determine when Plan A costs more than Plan B for a given number of minutes of phone use using linear inequalities. Learn step-by-step solutions for comparing pricing plans, including key formulas and concepts in algebra. Suitable for students in Grades 7-10.

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