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 Matt's dog walking business, we can break down his costs into a mathematical expression.

Part 1: Mathematical Expression

Let:

• \( x \) = number of 30-minute walks

The total cost \( C \) can be expressed as:

\[ C = 10 + 14x \]

Here:

• \( 10 \) is the one-time meeting fee,
• \( 14x \) is the cost per walk multiplied by the number of walks.

Part 2: Total Cost for 6 Walks

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

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

Now, calculate the cost:

1. First, calculate \( 14 \times 6 \):

\[ 14 \times 6 = 84 \]

2. Now, add the one-time fee:

\[ C = 10 + 84 = 94 \]

Conclusion

The total cost for 6 walks is $94.