¿Cuántas Cuadras Recorrió El Autobús?

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¿Cuántas cuadras recorrió el autobús?

Let's break down how to figure out how many blocks the bus traveled if Fernando paid $7.50 pesos and the bus charges $0.50 pesos for every 3 blocks. It's all about understanding the relationship between the cost and the distance covered. So, buckle up, guys, we're diving into some math!

Understanding the Problem

  • Fernando's Payment: Fernando paid a total of $7.50 pesos.
  • Bus Fare: The bus charges $0.50 pesos for every 3 blocks.
  • Goal: We need to find out the total number of blocks the bus traveled before Fernando got off.

Converting to Cents (Optional, but Helpful)

To make things a bit easier, especially if you're not a fan of decimals, we can convert everything to cents. Remember, 1 peso equals 100 centavos.

  • Fernando's Payment: $7.50 pesos * 100 centavos/peso = 750 centavos
  • Bus Fare: $0.50 pesos * 100 centavos/peso = 50 centavos

Converting to cents avoids working with decimals, which some people find easier. However, you can solve this problem using pesos directly – the choice is yours!

Calculating the Number of 3-Block Units

Now, we need to figure out how many "3-block units" Fernando paid for. We can do this by dividing the total amount he paid by the cost of each 3-block unit.

Using Pesos:

Number of 3-block units = Total payment / Cost per 3 blocks

Number of 3-block units = $7.50 / $0.50 = 15

Using Centavos:

Number of 3-block units = Total payment / Cost per 3 blocks

Number of 3-block units = 750 centavos / 50 centavos = 15

So, either way, we find that Fernando paid for 15 units of 3 blocks each. This is a crucial step, so make sure you understand how we arrived at this number.

Determining the Total Number of Blocks

We know that Fernando paid for 15 units, and each unit represents 3 blocks. To find the total number of blocks, we simply multiply the number of units by the number of blocks per unit.

Total number of blocks = Number of units * Blocks per unit

Total number of blocks = 15 * 3 = 45

Therefore, the bus traveled a total of 45 blocks before Fernando got off. And that's our final answer! This problem demonstrates a simple proportional relationship: the more you pay, the farther you travel. Understanding this relationship is key to solving similar problems.

Alternative Approach: Step-by-Step

If you prefer a more step-by-step approach, you can think about it this way:

  1. For $0.50 pesos, the bus travels 3 blocks.
  2. For $1.00 peso, the bus travels 3 blocks * 2 = 6 blocks.
  3. For $2.00 pesos, the bus travels 6 blocks * 2 = 12 blocks.
  4. For $4.00 pesos, the bus travels 12 blocks * 2 = 24 blocks.
  5. For $6.00 pesos, the bus travels 24 blocks + 12 blocks = 36 blocks
  6. To reach the final amount of $7.50, we need to add $1.50 to $6.00 We know that for $0.50 pesos, the bus travels 3 blocks, so for $1.50 pesos, the bus travels 3 blocks * 3 = 9 blocks
  7. For $7.50 pesos, the bus travels 36 blocks + 9 blocks = 45 blocks.

This step-by-step method can be helpful if you like to visualize the problem and build up to the solution incrementally. Choose the method that makes the most sense to you! Both approaches will lead you to the correct answer.

Common Mistakes to Avoid

  • Incorrect Unit Conversion: If you choose to convert to cents, make sure you do it correctly. A simple mistake in conversion can throw off your entire calculation.
  • Misinterpreting the Rate: Ensure you understand that $0.50 pesos is for every 3 blocks, not just for 3 blocks total. Pay close attention to the wording of the problem.
  • Arithmetic Errors: Double-check your multiplication and division to avoid simple calculation mistakes. It's easy to make a small error, especially when working under pressure.
  • Forgetting the Units: Always remember to include the units (blocks in this case) in your final answer. This helps to ensure that your answer makes sense and that you haven't missed anything.

Real-World Applications

This type of problem isn't just an abstract math exercise. It has real-world applications in everyday life. For example:

  • Calculating Taxi Fares: Taxi fares often have a base charge plus a per-mile or per-kilometer charge. You can use similar calculations to estimate the cost of a taxi ride.
  • Understanding Utility Bills: Utility companies often charge a fixed fee plus a per-unit charge for electricity, water, or gas. You can use these principles to understand how your utility bill is calculated.
  • Budgeting for Transportation: If you regularly use public transportation, you can use these types of calculations to budget your transportation expenses.

Practice Problems

To solidify your understanding, try solving these practice problems:

  1. Maria paid $12.00 pesos for the bus. If the bus charges $0.75 pesos for every 5 blocks, how many blocks did she travel?
  2. David traveled 60 blocks on the bus. If the bus charges $0.40 pesos for every 2 blocks, how much did he pay?
  3. A bus charges a flat rate of $2.00 pesos plus $0.25 pesos for every block. If a passenger paid $9.50 pesos, how many blocks did they travel?

Working through these practice problems will help you to master the concepts and build your confidence in solving similar problems in the future. Practice makes perfect! So, don't be afraid to tackle these problems and challenge yourself.

Conclusion

So, there you have it! Fernando traveled 45 blocks on the bus. By breaking down the problem into smaller steps and understanding the relationship between cost and distance, we were able to arrive at the correct answer. Remember to pay attention to the details, avoid common mistakes, and practice regularly to improve your problem-solving skills. Math can be fun, especially when you see how it applies to the real world. Keep practicing, and you'll become a math whiz in no time! Guys, I hope you found this explanation helpful and easy to understand. If you have any questions, feel free to ask!