To set up and solve this equation, let’s break down the information given in the problem:

• The technician worked for 4.75 hours.
• The cost of parts was $77.
• The total cost was $290.75.
• Let $x$ represent the cost of labor per hour.

Step 1: Set up the equation

The total cost of the repair includes both the labor cost and the cost of parts. The labor cost can be represented as $4.75x$, where $x$ is the hourly rate. Adding the parts cost to this gives the total cost:

$4.75x + 77 = 290.75$

Step 2: Solve for $x$

1. Subtract 77 from both sides:

   $4.75x = 290.75 - 77$ $4.75x = 213.75$

2. Divide both sides by 4.75 to find $x$:

   $x = \frac{213.75}{4.75}$ $x = 45$

Answer

The cost of labor per hour, $x$, is $45.

Would you like further details on this solution or have any questions?

Here are some related questions for further practice:

1. What would be the total cost if the hourly labor rate increased to $50?
2. If the technician worked for 6 hours instead of 4.75 hours, what would the new total cost be?
3. How much would the parts need to cost to keep the total at $290.75 if the hourly rate was $50?
4. What if the technician had worked only 3 hours? How would that change the hourly rate to maintain the same total cost?
5. How would the equation change if the total cost was $350 instead of $290.75?

Tip: Always double-check your work when solving for variables in equations involving multiple terms to ensure accuracy.