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 (2 points)


What is the total cost of 6 walks? Show all work to receive credit. (3 points)

(5 points)

Answer 1

To model the scenario with a mathematical expression, we can define the total cost \( C \) as a function of the number of walks \( w \).

1. Mathematical Expression: The total cost consists of a one-time meeting fee of $10 and a fee of $14 for each 30-minute walk. Therefore, the expression can be written as:

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

   where \( C(w) \) is the total cost and \( w \) is the number of walks.

2. Total Cost of 6 Walks: To find the total cost for 6 walks, we substitute \( w = 6 \) into our expression:

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

   Now calculate \( 14 \times 6 \):

   \[ 14 \times 6 = 84 \]

   Now plug this back into the expression:

   \[ C(6) = 10 + 84 \]

   Adding these together gives:

   \[ C(6) = 94 \]

   Therefore, the total cost of 6 walks is $94.

Summary of Points:

• Mathematical Expression: \( C(w) = 10 + 14w \) (2 points)
• Total Cost of 6 Walks: $94 (3 points)