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. Write the mathematical expression that models this scenario (2 points) What is the total cost of 6 walks? Show all work to receive credit. (3 points) (5 points)

Answer 1

To solve the problem, we first need to identify the components of the cost structure for Matt's dog walking business.

### Step 1: Write the Mathematical Expression

Matt charges a one-time meeting fee of $10 and an additional $14 for each 30-minute walk. Let's denote the number of walks as \( x \).

The total cost \( C \) of Matt’s service can be expressed mathematically as follows:

\[
C = 10 + 14x
\]

Where:
- \( 10 \) is the one-time meeting fee.
- \( 14x \) is the cost for \( x \) walks at a rate of $14 per walk.

### Step 2: Calculate the Total Cost for 6 Walks

Now, we need to find the total cost when \( x = 6 \).

Using the expression we derived:

\[
C = 10 + 14(6)
\]

Calculating the cost for the walks:

\[
C = 10 + 84
\]

Adding these amounts together gives us:

\[
C = 94
\]

### Final Answer

The total cost of 6 walks is \( \mathbf{94} \) dollars.

### Summary of Work
1. The mathematical expression for the total cost is \( C = 10 + 14x \).
2. For 6 walks, we substitute \( x = 6 \):
- \( C = 10 + 14(6) = 10 + 84 = 94 \).
3. Thus, the total cost for 6 walks is \( \mathbf{94} \) dollars.