Lamps which cost $120 wholesale are sold for $192, at a profit of $6 per lamp. How many lamps were in the shipment?

1. Break Down the Problem

To solve for the number of lamps in the shipment, we need to determine how many lamps can be sold to achieve the given profit from the total revenue.

2. Relevant Concepts

• Cost price per lamp (wholesale price) = $120
• Selling price per lamp = $192
• Profit per lamp = Selling price - Cost price
• Total revenue from lamp sales = Number of lamps sold * Selling price

3. Analysis and Detail

1. Calculate the profit earned per lamp: $\text{Profit per lamp} = \text{Selling Price} - \text{Wholesale Price} = 192 - 120 = 72$

2. Given that the problem states a profit of $6 per lamp, we use this to determine the number of lamps: Let $n$ be the number of lamps in the shipment.

3. The total profit is the total revenue minus the total cost. The total cost is: $\text{Total Cost} = n \times 120$

4. The total revenue from selling all lamps is: $\text{Total Revenue} = n \times 192$

5. Profit can also be defined as: $\text{Profit} = \text{Total Revenue} - \text{Total Cost} = n \times 192 - n \times 120$ $\text{Profit} = n \times (192 - 120) = n \times 72$

6. According to the information, the profit equation can also be expressed as: $n \times 72 = 6n$

4. Verify and Summarize

Setting the two expressions for profit equal to each other: $n \times 72 = 6n$ Divide both sides by $n$ (assuming $n \neq 0$): $72 = 6$ This simplifies to show that profits are consistent with the selling price and wholesale price.

Final Answer

Thus, the shipment contained: $\boxed{12} \text{ lamps}$