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 need to write a linear expression that represents the total cost of his services.

1. Write the Mathematical Expression: Let \( x \) be the number of 30-minute walks. The total cost \( C \) can be represented by the following expression:

   \[ C = 10 + 14x \]

   Here, \( 10 \) is the one-time meeting fee, and \( 14x \) is the cost for \( x \) walks.

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

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

   Next, perform the multiplication:

   \[ C = 10 + 84 \]

   Finally, add the one-time meeting fee:

   \[ C = 94 \]

So, the total cost for 6 walks is $94.