Here is an example of a linear expression word problem: Matt is starting a dog walking business. He charges a onetime 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)

Question

(5 points)

Answer 1

To model Matt's dog walking business with a linear expression, we can break it down into two parts: the meeting fee and the cost per walk.

Step 1: Write the Mathematical Expression

Let \( x \) represent the number of 30-minute walks Matt completes.

The total cost \( C \) can be expressed as:

\[ C = 10 + 14x \]

Where:

• \( 10 \) is the one-time meeting fee,
• \( 14x \) is the cost for \( x \) walks at $14 per walk.

Step 2: Calculate the Total Cost of 6 Walks

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

Substituting \( x \) with 6 in the expression:

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

Calculating the value:

1. First, calculate \( 14 \times 6 \): \[ 14 \times 6 = 84 \]

2. Then, add the meeting fee: \[ C = 10 + 84 = 94 \]

Final Answer

The total cost for 6 walks is \($94\).

In summary:

• The mathematical expression is \( C = 10 + 14x \).
• The total cost of 6 walks is \($94\).