Solving Tire Calculation Problem In A Parking Lot
In this article, we will solve a classic mathematical problem involving the calculation of the total number of tires in a parking lot containing cars and motorcycles. This type of problem is common in elementary mathematics and helps to develop basic arithmetic and logical reasoning skills. We'll break down the solution step by step to ensure a clear understanding. This article is perfect for students, teachers, and anyone who enjoys mathematical challenges.
Problem Statement
Imagine a parking lot filled with vehicles. Specifically, there are 10 cars and 15 motorcycles parked in this lot. Now, consider that each car has 4 tires, and each motorcycle has 2 tires. The question we need to answer is: what is the total number of tires in the parking lot?
To solve this, we will perform a simple calculation, multiplying the number of vehicles by the number of tires each vehicle has, and then summing these values. This is a straightforward application of multiplication and addition, essential skills in mathematics. So, let's delve into the detailed solution and explore the correct answer.
Step-by-Step Solution
To solve this problem efficiently, we need to break it down into smaller, manageable steps. This methodical approach not only helps in finding the correct answer but also enhances our understanding of the underlying concepts. Here's how we can tackle this problem:
1. Calculate the Total Number of Car Tires
The first step involves determining the total number of tires from the cars. We know there are 10 cars in the parking lot, and each car has 4 tires. To find the total, we multiply the number of cars by the number of tires per car:
Total car tires = Number of cars Ă— Tires per car
Total car tires = 10 Ă— 4
Total car tires = 40
Therefore, there are 40 tires in total from the cars.
2. Calculate the Total Number of Motorcycle Tires
Next, we calculate the total number of tires from the motorcycles. There are 15 motorcycles, and each has 2 tires. Similar to the previous step, we multiply the number of motorcycles by the number of tires per motorcycle:
Total motorcycle tires = Number of motorcycles Ă— Tires per motorcycle
Total motorcycle tires = 15 Ă— 2
Total motorcycle tires = 30
Thus, the motorcycles contribute 30 tires to the total.
3. Sum the Total Number of Tires
Now that we have the total number of tires from both cars and motorcycles, we need to add these two values together to find the overall total. We simply sum the tires from the cars (40) and the tires from the motorcycles (30):
Total tires = Total car tires + Total motorcycle tires
Total tires = 40 + 30
Total tires = 70
Therefore, there are a total of 70 tires in the parking lot.
Detailed Explanation of Each Step
1. Determining the Total Number of Car Tires
To accurately calculate the total number of tires on the cars, we use a straightforward multiplication principle. Understanding this principle is crucial for solving similar problems efficiently. We start with the known quantities: there are 10 cars in the parking lot, and each car is equipped with 4 tires. The core idea here is that each car contributes 4 tires to the total count. Thus, to find the cumulative number of tires from all cars, we need to multiply the number of cars by the number of tires each car possesses. This can be expressed mathematically as:
Total car tires = Number of cars Ă— Tires per car
Substituting the given values, we get:
Total car tires = 10 cars Ă— 4 tires/car
When we perform this multiplication, we are essentially adding the tires of each car together. It’s like saying 4 tires for the first car, 4 tires for the second car, and so on, for all 10 cars. The multiplication simplifies this repeated addition process. By multiplying 10 by 4, we arrive at the total number of tires that all the cars collectively have. Therefore, the calculation is simple:
Total car tires = 10 Ă— 4 = 40 tires
This means that the cars in the parking lot account for a total of 40 tires. This calculation is a fundamental step towards solving the overall problem, as it isolates the contribution of the cars before we consider the motorcycles. The simplicity of this calculation highlights the importance of understanding basic multiplication principles in everyday problem-solving. This step not only gives us a numerical value but also lays the groundwork for the subsequent steps where we will calculate the total tires for motorcycles and finally combine both results to find the overall total.
2. Calculating the Total Number of Motorcycle Tires
Moving on from the cars, our next crucial step is to determine the total number of tires contributed by the motorcycles. This calculation follows a similar logic to the previous one but uses different values that are specific to motorcycles. In the problem, we are given that there are 15 motorcycles, and each motorcycle has 2 tires. Just as with the cars, we need to find the aggregate number of tires from all the motorcycles. The principle we apply here is the same: we multiply the number of vehicles (in this case, motorcycles) by the number of tires each vehicle has.
Mathematically, this can be represented as:
Total motorcycle tires = Number of motorcycles Ă— Tires per motorcycle
Substituting the given values into this formula, we get:
Total motorcycle tires = 15 motorcycles Ă— 2 tires/motorcycle
Here, the multiplication signifies that we are adding the tires of each motorcycle. Since each motorcycle has 2 tires, multiplying by 15 is a shorthand for adding 2 tires fifteen times. This method is far more efficient than manual addition, especially when dealing with larger numbers. Performing the multiplication:
Total motorcycle tires = 15 Ă— 2 = 30 tires
This calculation shows that the motorcycles in the parking lot have a combined total of 30 tires. This number is essential as it represents the motorcycle's contribution to the overall tire count. Understanding how to compute this total separately is a key component of solving the larger problem. By isolating the motorcycle tires, we can accurately combine this number with the car tires calculated earlier to find the grand total. This step reinforces the concept of breaking down complex problems into simpler parts, each of which can be solved independently and then combined for a final solution. The calculation for motorcycles is a practical demonstration of applying basic multiplication in a real-world scenario, which helps to solidify mathematical understanding.
3. Summing the Total Number of Tires from Cars and Motorcycles
After successfully calculating the total number of tires from both cars and motorcycles, the final step in solving our problem is to combine these individual totals to find the grand total of tires in the parking lot. This step is crucial as it synthesizes the results of the previous calculations and provides the final answer to the original question. We have already determined that there are 40 tires from the cars and 30 tires from the motorcycles. The operation we need to perform here is simple addition: we add the total number of car tires to the total number of motorcycle tires.
This can be expressed mathematically as:
Total tires = Total car tires + Total motorcycle tires
Substituting the values we calculated earlier, we get:
Total tires = 40 tires + 30 tires
The addition here is straightforward. We are combining the two quantities to find the overall sum. In essence, we are counting all the tires together, regardless of whether they belong to cars or motorcycles. Performing the addition:
Total tires = 40 + 30 = 70 tires
This result indicates that there are a total of 70 tires in the parking lot, considering both cars and motorcycles. This final calculation not only provides the answer but also confirms the logical progression of our solution. By summing the individual totals, we ensure that we have accounted for all the tires present in the parking lot. This step underscores the importance of addition in combining different quantities to arrive at a comprehensive total. The simplicity of the addition belies its significance in the problem-solving process, highlighting how basic arithmetic operations can be effectively used to solve practical problems. The final total of 70 tires is the culmination of our step-by-step approach, demonstrating the power of methodical problem-solving in mathematics.
Correct Answer and Justification
Based on our step-by-step calculation, the correct answer to the question
