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. What is the total cost of 6 walks? Show all work.

Answer 1

To model the costs associated with Matt's dog walking business, we can break down the scenario as follows:

1. One-time meeting fee: This is a fixed cost of $10.
2. Per walk charge: Matt charges $14 for each 30-minute walk.

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

\[ C = 10 + 14x \]

where:

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

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

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

Now, calculate \( 14(6) \):

\[ 14 \times 6 = 84 \]

Next, we substitute this value back into the expression for \( C \):

\[ C = 10 + 84 = 94 \]

Therefore, the total cost of 6 walks is \( \boxed{94} \).