An automobile repair shop charged a customer \$1182, listing \$357 for parts and the remainder for labor. If the cost of labor is \$75 per hour, how many hours of labor did it take to repair the car?

Verified step by step guidance

1. Identify the total charge and the cost of parts. The total charge is \$1182, and the parts cost \$357.
2. Calculate the cost of labor by subtracting the cost of parts from the total charge: \(\$1182 - \$357\).
3. Let the number of labor hours be represented by the variable \(h\).
4. Set up the equation for labor cost using the hourly rate: \(75h = \text{cost of labor}\).
5. Solve for \(h\) by dividing the cost of labor by 75: \(h = \frac{\text{cost of labor}}{75}\).

Key Concepts

Setting Up an Equation

To solve word problems, translate the given information into an algebraic equation. Here, the total cost equals the sum of parts and labor costs, allowing you to express labor cost in terms of hours and set up an equation to find the unknown.

Solving Linear Equations

Once the equation is set, use algebraic methods to isolate the variable representing hours. This involves basic operations like subtraction and division to solve for the unknown quantity.

Unit Rate and Cost Interpretation

Understanding the meaning of unit rates, such as $75 per hour for labor, is essential. This helps convert the total labor cost into hours by dividing the labor cost by the hourly rate.