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.