https://file.aiquickdraw.com/mathbot/file/172840892053364ghjjc7.jpg

Let's break down the problem to form an inequality comparing the costs of plans A and B.

### Plan A:
- Cost per text: 10 cents.
- Total cost for sending and receiving $ x $ texts = $ 0.10x $ (where $ x $ is the number of texts).

### Plan B:
- Monthly fee: 12 dollars.
- Additional cost per text: 2 cents.
- Total cost for sending and receiving $ x $ texts = $ 12 + 0.02x $.

To find the inequality representing when plan A is cheaper than plan B, we set up the inequality as:

\[
0.10x < 12 + 0.02x
\]

### Solving the inequality:
1. Subtract $ 0.02x $ from both sides:
   \[
   0.10x - 0.02x < 12
   \]
   \[
   0.08x < 12
   \]

2. Divide both sides by 0.08:
   \[
   x < \frac{12}{0.08}
   \]
   \[
   x < 150
   \]

### Interpretation:
It is cheaper to use Plan A if the person sends fewer than 150 texts.

Would you like more details or have any questions about this solution?

Here are 5 related questions to deepen understanding:
1. How would the inequality change if the cost per text for Plan A was 15 cents instead of 10?
2. How many texts would make the two plans cost exactly the same?
3. What would happen if Plan B had no monthly fee but a higher per-text cost?
4. How would the inequality change if Plan B's monthly fee increased to $15?
5. What happens if you only send half as many texts, does Plan A remain cheaper?

### Tip:
When comparing plans with fixed and variable costs, always check at what point one plan becomes more economical.

A cell phone company offers two texting plans. People who use plan A pay 10 cents for each text sent or received. People who use plan B pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received. Write an inequality to represent the fact that it is cheaper for someone to use plan A than plan B. Use x to represent the number of texts they send.

Learn how to compare two cell phone plans using a linear inequality. Plan A costs 10 cents per text, while Plan B has a $12 monthly fee with an additional 2 cents per text. Find out when Plan A becomes cheaper using algebra and inequalities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation