Calculating Total Car Cost A Mathematical Problem
In this article, we will embark on a mathematical journey to unravel the costs associated with repairing and selling a car. We will dissect the expenses incurred, the selling price, and ultimately, determine the total cost of the car. This is a practical application of basic arithmetic, showcasing how math is used in everyday scenarios. Let's delve into the problem and break it down step-by-step.
Understanding the Initial Expenses
Our mathematical exploration begins with identifying the initial expenses incurred in repairing the car. We are given three specific costs: $86 spent on tires, $62 spent on painting, and $19, although the purpose of this $19 is not specified, we assume it's also a repair or maintenance cost. The first step in our journey is to calculate the total repair cost by adding these individual expenses. This involves simple addition, a fundamental operation in mathematics. By accurately summing these values, we lay the foundation for determining the overall cost of the car. The challenge here lies not just in the arithmetic, but in understanding how these costs contribute to the final price. This is where mathematical reasoning becomes essential. Let's perform the calculation:
$86 (Tires) + $62 (Painting) + $19 (Unspecified Repair) = $167
Therefore, the total amount spent on repairing the car is $167. This figure is crucial as we move forward, as it forms a significant component of the car's overall cost. Understanding this expense is key to understanding the profitability, or in this case, the loss incurred in the sale.
Unveiling the Selling Price and the Loss
Now, let's turn our attention to the selling price and the loss incurred. The problem states that the car was sold for $136 less than the total cost and fetched $854. This provides us with a crucial piece of information – the selling price. We know the selling price was $854, but more importantly, we know the relationship between the selling price and the total cost. The car was sold at a loss of $136, meaning the selling price was $136 lower than the total cost. To decipher the total cost, we need to reverse this loss. We can do this by adding the loss amount to the selling price. This step involves understanding the concept of profit and loss, a common application of mathematics in business and finance. By adding the loss back to the selling price, we effectively undo the price reduction and arrive at the total cost. This is a fundamental principle in financial calculations and is crucial for businesses to understand their profitability. Let's perform this calculation:
$854 (Selling Price) + $136 (Loss) = $990
This calculation reveals that the total cost of the car, before considering the repair expenses, was $990. This is a significant milestone in our mathematical journey, as it provides us with a baseline figure to which we can add the repair costs to find the total investment in the car.
Calculating the Total Cost: The Final Equation
We are now at the final equation of our mathematical journey: determining the total cost of the car. We have previously calculated two key figures: the total repair cost ($167) and the initial cost of the car before repairs ($990). To find the total cost, we simply need to add these two figures together. This step encapsulates the entire problem, bringing together all the individual expenses and the initial cost to provide a comprehensive understanding of the car's total investment. This calculation highlights the importance of considering all costs when evaluating a financial transaction, whether it's a car repair and sale or any other business venture. Failing to account for all expenses can lead to an inaccurate assessment of profitability and potentially poor decision-making. This final step underscores the practical application of mathematics in managing finances and making informed choices. Let's execute the calculation:
$990 (Initial Cost) + $167 (Repair Costs) = $1157
Therefore, the total cost of the car, encompassing both the initial cost and the repair expenses, is $1157. This figure represents the total investment made in the car before it was sold.
The Answer: Unveiling the Total Cost
In conclusion, after carefully analyzing all the expenses and the selling price, we have successfully determined the total cost of the car. By meticulously adding the repair costs to the initial cost derived from the selling price and loss, we arrived at the final figure. The total cost of the car is $1157. This mathematical exercise not only provides us with the answer to the problem but also demonstrates the practical application of basic arithmetic in real-world scenarios. Understanding how to calculate costs, losses, and selling prices is crucial in various financial situations, from personal budgeting to business management. This problem serves as a valuable lesson in the importance of careful calculation and mathematical reasoning in everyday life.
This mathematical journey has taken us through the process of calculating the total cost associated with repairing and selling a car. We began by identifying the individual repair expenses, then deciphered the initial cost of the car by considering the selling price and the loss incurred. Finally, we combined these figures to arrive at the total cost. This exercise underscores the importance of mathematics in everyday scenarios and highlights the practical application of basic arithmetic. The ability to accurately calculate costs and understand financial transactions is a valuable skill, whether in personal finances or in business. By breaking down complex problems into smaller, manageable steps, we can effectively solve them and gain a deeper understanding of the underlying principles. This problem serves as a reminder that mathematics is not just an academic subject, but a powerful tool that can be used to navigate the complexities of the real world.
Breaking Down the Solution for Clarity
To further solidify our understanding, let's recap the steps we took in this mathematical endeavor:
- Calculate Total Repair Costs: We added the expenses for tires, painting, and the unspecified repair to determine the total repair cost.
- Determine Initial Cost: We added the loss incurred to the selling price to find the initial cost of the car before repairs.
- Calculate Total Cost: We added the total repair costs to the initial cost to find the overall investment in the car.
By following these steps, we systematically deconstructed the problem and arrived at the correct answer. This approach highlights the importance of methodical problem-solving in mathematics and other fields.