Question

Solve. A sofa with an initial price of \(\$ 699.99\) is marked \(35 \%\) off. What are the discount amount and final price?

Short answer

Answer: The discount amount is $245.00, and the final price of the sofa is $454.99.

Step-by-step solution

Finding the discount amount

To find the discount amount, multiply the initial price by the discount percentage. In this case, the initial price is \(699.99, and the discount percentage is \)35\%$. To convert the percentage to a decimal, divide it by 100. Discount amount = Initial price * Discount percentage Discount amount = 699.99 * (35/100)

Calculate the discount amount

Now, we can compute the discount amount using the formula from Step 1. Discount amount = 699.99 * (35/100) = 699.99 * 0.35 = 244.997 Since money values are typically rounded to two decimal places, the discount amount should be approximately $245.00.

Finding the final price

Now that we know the discount amount, we can find the final price by subtracting the discount amount from the initial price. Final price = Initial price - Discount amount Final price = 699.99 - 245.00

Calculate the final price

Use the formula from Step 3 to find the final price: Final price = 699.99 - 245.00 = 454.99 Therefore, the discount amount is \(245.00, and the final price of the sofa after the discount is \)454.99.

Key concepts

Discount Calculation

Discount calculation is a straightforward process, often used in sales to determine how much a price is reduced. To find the discount, we first need to convert the given percentage into a decimal by dividing by 100. This is because percentages are out of 100, and decimals provide a direct way to multiply with our initial values.
In this example, the discount percentage is 35%. To convert this percentage to a decimal, divide 35 by 100:

• 35% = 35/100 = 0.35

Now that you have the decimal form, multiply it by the initial price of the item (in this case, the sofa priced at $699.99) to find the discount amount.
Therefore, the discount amount can be calculated as:

• Discount amount = Initial price × Discount decimal = 699.99 × 0.35 = 244.997

Typically, money values are rounded to two decimal places, so in this case, the discount amount is approximately $245.00.

Initial Price and Final Price

Understanding the difference between the initial price and final price is crucial in calculations involving discounts. The initial price is the original cost of the item before any discounts are applied. In our problem, the initial price of the sofa is $699.99.
To calculate the final price, which is the price a customer will pay post-discount, we subtract the discount amount from the initial price. This gives the remaining amount that reflects the cost after the reduction.
Here's how we find the final price:

• Initial price = $699.99
• Discount amount = $245.00
• Final price = Initial price - Discount amount = $699.99 - $245.00 = $454.99

The final price, therefore, is $454.99, meaning the customer will only need to pay this amount to purchase the sofa.

Decimal Conversion

Decimal conversion is a fundamental step in percentage problems. It involves changing percentages into decimals, allowing for easier multiplication and calculation in determining discounts.
To convert a percentage into a decimal, simply divide by 100. For example:

• A percentage of 35% becomes a decimal by calculation: 35/100 = 0.35

This conversion is essential, as multiplying with decimals directly provides the amount that should be removed from the initial price (the discount amount) or added to the initial cost in other scenarios.
This concept not only applies to discounts but is useful in various financial calculations like interest rates, tax computations, and markups. By mastering decimal conversion, you'll handle a wide array of percentage problems with ease in real-world situations.