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.

Question

Write the mathematical expression that models this scenario


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

Answer 1

To model the scenario mathematically, we can break down the costs into components.

1. Meeting Fee: This is a one-time charge, which is $10.
2. Cost per Walk: Matt charges $14 for each 30-minute walk.

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

\[ C = 10 + 14x \]

where:

• \( C \) is the total cost,
• \( 10 \) is the one-time meeting fee,
• \( 14x \) is the cost for \( x \) walks.

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

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

Calculating \( 14 \times 6 \):

\[ 14 \times 6 = 84 \]

Now, substitute that value back into the equation:

\[ C = 10 + 84 = 94 \]

Therefore, the total cost for 6 walks is:

\[ \boxed{94} \]