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The question in the image is about comparing two pricing plans for truck rental, which involves solving a two-step linear inequality.

**Problem Recap:**
- Company A charges a flat fee of **$67** for unlimited mileage.
- Company B charges an initial fee of **$55** and an additional **$0.80** per mile.

You are asked to find when Company A will charge less than Company B based on the number of miles driven, represented by $ m $. The goal is to form an inequality to represent this and solve for $ m $.

### Step 1: Set up the inequality
Let $ m $ be the number of miles driven.
- Company A's cost is a constant **$67**.
- Company B's cost is **$55 + 0.80m** (where $ m $ is the number of miles).

To find when Company A is cheaper than Company B, set up the inequality:
\[
67 < 55 + 0.80m
\]

### Step 2: Solve the inequality
1. Subtract **55** from both sides:
   \[
   67 - 55 < 0.80m
   \]
   Simplifying:
   \[
   12 < 0.80m
   \]

2. Divide both sides by **0.80** to isolate $ m $:
   \[
   \frac{12}{0.80} < m
   \]
   Simplifying the division:
   \[
   15 < m
   \]

### Final Solution:
\[
m > 15
\]
This means Company A will charge less than Company B when the number of miles driven exceeds **15 miles**.

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Do you want further details or have any questions?

### Related Questions:
1. How would the inequality change if Company B increased its base fee?
2. What would happen if Company A introduced a per-mile charge as well?
3. How could this inequality be represented graphically?
4. What would the inequality look like if both companies had the same base charge?
5. What happens if the per-mile cost of Company B decreases?

**Tip:** Always check which company's pricing structure offers a flat rate or per-unit rate when comparing options like this.

Mai is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices: Company A charges $67 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.80 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

Learn how to solve a linear inequality problem involving cost comparison between two truck rental companies. Understand the step-by-step process to determine for what mileages Company A charges less than Company B.

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