Car Price Reduction Calculation Explained
Hey guys! Ever wondered how car price reductions work? Let's break down a real-world example to make it super clear. We’re diving into a scenario where a car dealership has slashed the price of a car, and we’re going to figure out the new price after the discount. So, buckle up and let’s get started!
(a) Fill in the Blank to Write the New Price in Terms of the Original Price Write Your Answer as a Decimal
Understanding the Percentage Reduction
In this part, we're focusing on expressing the new price as a decimal multiple of the original price. The main idea here is understanding percentage reductions. When a car's price is reduced by 14%, it means the new price is 100% - 14% = 86% of the original price. This is a crucial concept to grasp, as it forms the foundation for our calculations. To convert this percentage into a decimal, we divide 86 by 100, which gives us 0.86. So, the blank can be filled with 0.86, representing the portion of the original price that the new price constitutes. Thinking about this in everyday terms, if something is 14% off, you’re essentially paying 86% of the original cost. This is a common scenario when you're shopping for deals, whether it's cars, clothes, or electronics. It's always good to know how to calculate these discounts quickly to make sure you're getting the best price. Understanding this concept also helps in budgeting and making informed financial decisions. For example, if you have a budget in mind for a car, knowing how to calculate discounts can help you determine if a particular deal fits within your budget. Moreover, this skill is transferable to many other areas of life, such as calculating sale prices at stores, understanding investment returns, or even figuring out tips at restaurants. Remember, the key is to convert the percentage reduction into a decimal by subtracting it from 100% and then dividing by 100. This gives you the factor by which you multiply the original price to get the new price. So, in our case, the new price is 0.86 times the original price.
Calculating the New Price
Now that we understand the concept of expressing the new price as a decimal of the original price, let's dive into how we apply this in practice. To calculate the new price, we use the formula: New Price = Decimal Multiplier × Original Price. In our case, the decimal multiplier is 0.86 (as we calculated earlier), and the original price is $45,500. So, we multiply these two values together: New Price = 0.86 × $45,500. This calculation is pretty straightforward but super important for getting the final answer. When you do the math, you’ll find that the new price is $39,130. This is the actual price you would pay after the 14% discount. Understanding how to calculate this is valuable because it allows you to quickly determine the actual cost of an item after a discount, which is super useful when you're comparing prices or trying to stay within a budget. Think about it this way: if you're at a car dealership and they offer you a discount, you can quickly calculate the new price yourself to make sure the numbers add up correctly. This also helps you avoid being misled by advertisements that might not clearly state the final price. Furthermore, this skill extends beyond just buying cars. It’s applicable to any situation where you encounter discounts or sales, whether it's buying a new TV, booking a vacation, or even grocery shopping. The ability to quickly calculate the discounted price helps you make informed decisions and ensures you’re getting a fair deal. So, remember the formula: New Price = Decimal Multiplier × Original Price. It’s a handy tool to have in your financial toolkit.
Practical Applications and Real-World Scenarios
The ability to calculate discounted prices, like the one we just worked through, has countless practical applications. Imagine you're shopping for a new laptop, and you see one that's marked down by 20%. You can quickly use the method we discussed to figure out the actual price you'll pay. This is super useful for comparing deals and making sure you're getting the best value for your money. Let's say the laptop's original price is $1200. A 20% discount means you're paying 80% of the original price (100% - 20% = 80%). Converting 80% to a decimal gives you 0.80. So, the discounted price is 0.80 × $1200 = $960. Knowing this, you can compare this price with other laptops on the market and see if it's a good deal. This skill is also crucial when you're dealing with larger purchases, like a car or a house. Even small percentage discounts can translate to significant savings. For instance, if you're buying a house and you negotiate a 1% reduction in the price, that could save you thousands of dollars. The same principle applies to investments. Understanding how to calculate percentage changes can help you track the performance of your investments and make informed decisions about buying and selling. For example, if your stock portfolio increases in value by 15%, you can calculate the actual dollar amount of your gains. Moreover, this skill is essential in everyday situations, such as calculating tips at restaurants or splitting bills with friends. If you're dining out and want to leave a 18% tip, you can easily calculate it by multiplying the bill amount by 0.18. In short, understanding how to work with percentages and discounts is a fundamental life skill that can save you money and help you make better financial decisions across various aspects of your life.