A) 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)

Answer 1

To model Matt's dog walking business, we can create a linear expression that captures both the one-time meeting fee and the per-walk charge.

A) Mathematical Expression

Let \( x \) represent the number of 30-minute walks. The total cost \( C \) can be expressed as:

\[ C = 10 + 14x \]

Where:

• \( 10 \) is the one-time meeting fee.
• \( 14x \) is the cost for the walks (with \( x \) being the number of walks).

B) Total Cost of 6 Walks

To find the total cost of 6 walks, we will substitute \( x = 6 \) into the expression:

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

Now we calculate the total cost step by step:

1. Calculate \( 14 \times 6 \): \[ 14 \times 6 = 84 \]

2. Now add the one-time fee: \[ C = 10 + 84 = 94 \]

Therefore, the total cost of 6 walks is:

\[ \boxed{94} \]