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

Answer 1

To create a mathematical expression for Matt's dog walking business, we need to account for both the one-time fee and the variable cost for each walk.

1. **Identify the fixed and variable costs:**
- One-time meeting fee: $10
- Charge per walk: $14
- Let \( x \) represent the number of walks.

2. **Write the expression:**
The total cost \( C \) can be expressed as:
\[
C = 10 + 14x
\]
where \( 10 \) is the meeting fee and \( 14x \) is the total charge for \( x \) walks.

3. **Calculate the total cost for 6 walks:**
Substitute \( x = 6 \) into the expression:
\[
C = 10 + 14 \cdot 6
\]
Calculate \( 14 \cdot 6 \):
\[
14 \cdot 6 = 84
\]
Now substitute back into the expression:
\[
C = 10 + 84
\]
Add the two amounts together:
\[
C = 94
\]

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