Let's define the variables and set up an equation based on the given information:

• Let $x$ be the cost of labor per hour.
• The technician worked for 2.5 hours.
• The total labor cost would then be $2.5x$.
• The cost of parts was $100.
• The total cost was $237.50.

The equation that represents the total cost is:

$2.5x + 100 = 237.50$

To solve for $x$, follow these steps:

1. Subtract 100 from both sides of the equation:

$2.5x = 237.50 - 100$

$2.5x = 137.50$

2. Divide both sides by 2.5 to isolate $x$:

$x = \frac{137.50}{2.5}$

$x = 55$

So, the cost of labor per hour is $55.

Would you like more details on how this was calculated, or do you have any questions?

Here are 5 related questions for further practice:

1. If the technician worked for 3 hours, and the parts cost remained $100, what would the total cost be?
2. What if the parts cost $150 instead of $100, how would that affect the hourly labor cost if the total still needs to be $237.50?
3. How would the equation change if the technician gave a discount of $20 on the total labor cost?
4. If the total cost had been $250, with the same hours worked and parts cost, what would the hourly labor cost be?
5. How much would Amelia pay if the labor cost per hour was $60 and the technician worked for 2.5 hours, with parts costing $100?

Tip: When setting up an equation, always identify what the variable represents and ensure that all parts of the problem are accounted for in the equation.