Calculating Discounts And Sales Tax On Headphones

Let's break down the steps to figure out if you can snag those headphones with your gift certificate. We'll cover the discount amount, the final sale price, and how sales tax comes into play. Understanding these calculations is crucial for making informed purchasing decisions and managing your budget effectively. This scenario presents a practical application of percentages, discounts, and sales tax, concepts that are fundamental in everyday financial transactions. By working through this example, you'll gain a clearer understanding of how these calculations impact the final cost of a product, empowering you to make smarter choices when shopping.

a) Calculating the Discount

The first step in determining the final price of the headphones is to calculate the discount. You've found a pair of headphones priced at $43.00, and they're on sale for 20% off. To find the discount amount, you need to calculate 20% of $43.00. Understanding percentages is essential here. A percentage is simply a way of expressing a number as a fraction of 100. So, 20% means 20 out of 100, or 20/100. To calculate the discount, we convert the percentage to a decimal by dividing it by 100 (20 / 100 = 0.20). Then, we multiply the original price by this decimal: $43.00 * 0.20 = $8.60. Therefore, the discount amount is $8.60. This means you'll save $8.60 off the original price of the headphones. Knowing how to calculate discounts allows you to quickly assess the true savings on a product and compare prices effectively. It's a valuable skill for budgeting and making the most of sales and promotions. Furthermore, this calculation demonstrates the practical application of percentage calculations in real-world scenarios. Mastering this skill can help you in various situations, from understanding markdowns at a clothing store to calculating interest on a loan.

b) Determining the Sale Price

Now that we've calculated the discount, we can determine the sale price of the headphones. The sale price is the original price minus the discount amount. In this case, the original price is $43.00, and the discount is $8.60. To find the sale price, we subtract the discount from the original price: $43.00 - $8.60 = $34.40. So, the sale price of the headphones is $34.40. This is the price you'll pay before any applicable taxes are added. Calculating the sale price after a discount is a crucial step in determining the affordability of an item. It allows you to see the actual cost you'll incur and helps you compare prices across different retailers or promotions. This skill is especially important during sales events or when shopping with coupons or promotional codes. By knowing how to calculate the sale price, you can ensure you're getting the best deal possible. Moreover, this calculation reinforces the concept of subtraction and its application in real-world financial scenarios. It's a fundamental skill that is used in various contexts, such as managing personal finances, budgeting, and making informed purchasing decisions.

c) Calculating the Sales Tax

The final step in determining the total cost of the headphones is to calculate the sales tax. Sales tax is a percentage of the sale price that is added to the cost of goods and services. In this scenario, the sales tax rate is 13%. To calculate the sales tax, we need to find 13% of the sale price, which we calculated to be $34.40. Similar to calculating the discount, we first convert the percentage to a decimal by dividing it by 100 (13 / 100 = 0.13). Then, we multiply the sale price by this decimal: $34.40 * 0.13 = $4.472. Since we're dealing with money, we round this to the nearest cent, which is $4.47. Therefore, the sales tax added to the sale price is $4.47. Understanding how sales tax is calculated is essential for accurate budgeting and financial planning. Sales tax can significantly impact the total cost of a purchase, especially for higher-priced items. By knowing how to calculate sales tax, you can avoid surprises at the checkout and make informed decisions about your spending. This calculation also reinforces the importance of rounding in financial calculations to ensure accuracy and avoid discrepancies. Furthermore, it highlights the practical application of percentage calculations in determining the final cost of goods and services, a skill that is valuable in various aspects of personal and professional life.

Now, let's add the sales tax to the sale price to find the final cost: $34.40 (sale price) + $4.47 (sales tax) = $38.87. So, the total cost of the headphones, including sales tax, is $38.87.

Can You Use Your Gift Certificate?

You have a $40 gift certificate. The total cost of the headphones, including sales tax, is $38.87. Since $38.87 is less than $40, you have enough on your gift certificate to purchase the headphones! You'll even have a little bit of credit left over on your gift certificate. This final step demonstrates how all the previous calculations come together to help you make a purchasing decision. By understanding discounts, sale prices, and sales tax, you can confidently assess whether you can afford an item and how best to utilize your available resources, such as gift certificates or coupons. This skill is invaluable for effective budgeting and financial management, allowing you to make informed choices and maximize the value of your money.