Question

here is an example of a linear expression word problem matt is starting a dog walking business he charges a one time meeting fee of $10 and $14 per 30 minute walk,

Answer 1

To set up a linear expression for Matt's dog walking business, we will break down the components of the costs involved:

1. **One-time meeting fee**: This is a fixed cost of $10.
2. **Cost per walk**: This is a variable cost where Matt charges $14 for each 30-minute walk.

Let's define a variable:
- Let \( x \) represent the number of 30-minute walks Matt completes.

Now, we can create a linear expression to represent Matt's total charges for his services based on the number of walks he provides:

\[
\text{Total Cost} = \text{One-time fee} + \text{Cost per walk} \times \text{Number of walks}
\]

Putting in the values we have:

\[
\text{Total Cost} = 10 + 14x
\]

Where:
- \( 10 \) is the one-time meeting fee,
- \( 14x \) is the cost for \( x \) walks.

### Example Problem:
If a customer wants to book 5 walks, we can find the total cost using the expression we formulated:

\[
\text{Total Cost} = 10 + 14(5) = 10 + 70 = 80
\]

So, the total cost for 5 walks, including the meeting fee, would be $80.