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 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.