A repair bill on a sailboat came to \$2356, including \$826 for parts and the remainder for labor. If the cost of labor is \$90 per hour, how many hours of labor did it take to repair the sailboat?

Verified step by step guidance

1. Identify the total cost of the repair bill, which is \$2356, and the cost of parts, which is \$826.
2. Calculate the cost of labor by subtracting the cost of parts from the total bill: \$2356 - \$826 = \text{labor cost}$.
3. Let the number of labor hours be represented by \(h\). Since labor costs \$90 per hour, the total labor cost can be expressed as \$90h$.
4. Set up the equation for labor cost: \$90h = \text{labor cost}$ (from step 2).
5. Solve for \(h\) by dividing both sides of the equation by 90: \(h = \frac{\text{labor cost}}{90}\).

Key Concepts

Understanding Total Cost Breakdown

The total cost is composed of parts and labor costs. To find the labor cost, subtract the cost of parts from the total bill. This step isolates the amount spent specifically on labor.

Solving Linear Equations

Once the labor cost is known, use a simple linear equation to find the number of labor hours. Divide the labor cost by the hourly rate to solve for the unknown variable representing hours worked.

Unit Rate and Division

The hourly labor rate is a unit rate, meaning cost per one hour. Dividing the total labor cost by this unit rate converts total cost into total hours, linking monetary values to time.