Un agente de negocios compró algunos carros por $4,000. El los vendió por $5,000 ganando $50 en cada automóvil. Cuántos carros tuvo en la transacción?

1. ### Break Down the Problem

We need to determine how many cars the agent bought and sold in the transaction. Given the total cost, selling price, and profit per car, we can set up the problem with variables.

2. ### Relevant Concepts

• Let $n$ be the number of cars.
• Total cost of the cars: $4000$ dollars.
• Selling price of each car: $5000/n$ dollars (since the total selling price will be the total revenue divided by the number of cars).
• Profit per car: $50$ dollars.

The profit can be calculated as: $\text{Profit} = \text{Selling Price} - \text{Cost Price}$

3. ### Analysis and Detail

1. The total cost for $n$ cars is: $\text{Cost Price per car} = \frac{4000}{n}$

2. Using the profit equation: $50 = \frac{5000}{n} - \frac{4000}{n}$

3. Simplifying the equation: $50 = \frac{5000 - 4000}{n}$ $50 = \frac{1000}{n}$

4. Solving for $n$: $n = \frac{1000}{50}$ $n = 20$

4. ### Verify and Summarize

Let's verify our answer:

• If the agent sold 20 cars, then:
  • Cost price per car = $\frac{4000}{20} = 200$ dollars.
  • Selling price per car = $\frac{5000}{20} = 250$ dollars.
  • Profit per car = $250 - 200 = 50$ dollars, which matches the problem statement.

Final Answer

The agent had 20 cars in the transaction.