https://file.aiquickdraw.com/mathbot/file/1728936050464mtqcn6je.jpg

Let's break down the problem shown in the image.

The phone company offers two plans:

- **Plan A**: Monthly fee of $25 plus 6 cents per minute of phone use.
- **Plan B**: Monthly fee of $31.90 plus 5 cents per minute of phone use.

We need to find for which number of phone use minutes (denoted by $ m $) Plan A will cost **less** than Plan B. This leads us to set up an inequality comparing the total cost of both plans.

1. **Cost of Plan A**: $ 25 + 0.06m $ (where $ m $ is the number of minutes)
2. **Cost of Plan B**: $ 31.90 + 0.05m $

We need to solve the inequality where Plan A's cost is less than Plan B's:

\[
25 + 0.06m < 31.90 + 0.05m
\]

### Solving the inequality:
1. Subtract $ 0.05m $ from both sides:

\[
25 + 0.01m < 31.90
\]

2. Subtract 25 from both sides:

\[
0.01m < 6.90
\]

3. Divide by 0.01 to isolate $ m $:

\[
m < \frac{6.90}{0.01} = 690
\]

### Conclusion:
Plan A will cost less than Plan B when the number of phone minutes is **less than 690 minutes**.

---

Do you have any questions or need further explanation? 

Here are some related questions:
1. What if the monthly fee in Plan B increased?
2. How would the inequality change if the per-minute costs were the same?
3. What happens if the fees are reduced but the per-minute rates increase?
4. How would you graph the cost comparison of the two plans?
5. Can you think of another scenario where similar inequalities might be useful?

**Tip**: Always double-check your inequality setup to ensure you're comparing the right quantities!

For what amounts of monthly phone use will Plan A cost less than Plan B? Plan A: $25 per month + 6 cents per minute; Plan B: $31.90 per month + 5 cents per minute.

Learn how to solve a cost comparison between two phone plans, where Plan A charges a monthly fee of $25 with 6 cents per minute, and Plan B charges $31.90 with 5 cents per minute. Solve for the number of minutes where Plan A costs less than Plan B. Suitable for Grades 7-9.

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