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


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

Answer 1

To model the scenario mathematically, we can break down the costs into components.

1. Meeting Fee: This is a one-time charge, which is $10.
2. Cost per Walk: Matt charges $14 for each 30-minute walk.

Let $x$ represent the number of walks. The total cost $C$ can then be expressed as:

$$C=10+14x$$

where:

• $C$ is the total cost,
• $10$ is the one-time meeting fee,
• $14x$ is the cost for $x$ walks.

Now, to find the total cost for 6 walks, we substitute $x=6$ into the expression:

$$C=10+14(6)$$

Calculating $14\times 6$:

$$14\times 6=84$$

Now, substitute that value back into the equation:

$$C=10+84=94$$

Therefore, the total cost for 6 walks is:

$$\boxed{{\displaystyle 94}}$$