A woodworker wants to earn at least $25.00 per hour making and selling cabinets.  He plans to sell the cabinets for $500.00  He pays $125 for materials.  Write and solve an inequality that represents how many hours the woodworker can spend building the cabinets.

Let's define the variables and set up an inequality to represent the situation:

- Let $ h $ represent the number of hours the woodworker spends building the cabinets.
- The woodworker sells each cabinet for $500. However, he spends $125 on materials, so his profit per cabinet is $ 500 - 125 = 375 $ dollars.
- The woodworker wants to earn at least $25 per hour.

Now, the total money he makes for building one cabinet must be at least $25 for every hour he spends on it. Therefore, the inequality can be written as:

\[
\frac{375}{h} \geq 25
\]

To solve this inequality, we will multiply both sides by $ h $ to eliminate the denominator:

\[
375 \geq 25h
\]

Next, divide both sides by 25 to isolate $ h $:

\[
h \leq \frac{375}{25}
\]

\[
h \leq 15
\]

### Solution:
The woodworker can spend **no more than 15 hours** building the cabinet if he wants to earn at least $25 per hour.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. What if the woodworker wants to earn at least $30 per hour? How would the inequality change?
2. How much total profit will the woodworker make if he builds 3 cabinets in 10 hours each?
3. What if the cost of materials increases to $150? How does that affect the inequality?
4. If the woodworker finishes a cabinet in 12 hours, how much does he earn per hour?
5. How would the inequality change if the woodworker plans to sell the cabinet for $600 instead?

**Tip:** When solving inequalities, remember to reverse the inequality sign when multiplying or dividing by a negative number.

A woodworker wants to earn at least $25.00 per hour making and selling cabinets. He plans to sell the cabinets for $500.00. He pays $125 for materials. Write and solve an inequality that represents how many hours the woodworker can spend building the cabinets.

Discover how to solve an inequality problem where a woodworker wants to earn at least $25 per hour making cabinets. This problem uses algebra to set up the inequality and calculate how many hours the woodworker can spend building each cabinet, considering material costs and profit.

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