Question

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)

(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)