Problem 53 - Algebra A Combined Function

Question

Nordstrom advertised a \(25 \%\) -off sale. If a London Fog coat originally sold for \(\$ 256,\) find the decrease in price and the sale price.

Step-by-Step Solution

Answer

The decrease in price is $64, and the sale price is $192.

Step 1: Calculate the Discount Amount

To find the decrease in price, we need to calculate what 25% of the original price (\(256) is. This is done by multiplying the original price by the discount rate: \[ 256 \times 0.25 = 64 \] The decrease in price is \)64.

Step 2: Calculate the Sale Price

Now, you need to subtract the discount amount from the original price to find the sale price. The original price is \(256, and the discount is \)64:\[ 256 - 64 = 192 \] So, the sale price of the coat is $192.

Key Concepts

Understanding Discount Calculations

When it comes to shopping, discounts are our friend. A discount reduces the original price of an item, making it more affordable. To calculate a discount, you need to know the original price and the discount rate (usually expressed as a percentage). For our exercise, the original price of the coat is $256 and the discount rate is 25%. To find the discount amount, simply multiply the original price by the discount rate expressed as a decimal. So, we convert 25% to its decimal form, which is 0.25.

• Formula: Discount Amount = Original Price × Discount Rate
• Calculation: $256 × 0.25 = $64

If you subtract this discount amount from the original price, you will get the sale price. But first, it is key to understand this concept so you can apply it to any discounted situation. The idea remains the same: Multiply and then subtract.
The discount shows us how much we're saving, which in our case is $64.

Calculating the Sale Price

The sale price is simply the new, reduced price after the discount has been applied. To determine the sale price, subtract the discount amount from the original price. This process reveals how much you actually pay after the discount has been taken into account. Remember the steps:

• Start with the original price (for example, \(256).
• Subtract the discount amount (\)64, as calculated).

This gives us the sale price: \[ 256 - 64 = 192\] So, the coat's sale price during the discount period is $192. It’s the amount you pay at the checkout.
Understanding how to calculate the sale price confirms you aren't overpaying or getting any surprises at checkout. This is straightforward once you have calculated the discount amount; the last step is just simple subtraction. A bit of math for big savings!

Determining Original Price

The original price is the cost of an item before any discounts. It represents the item's full value when there is no sale. In many shopping experiences, original prices are marked on the price tag, providing a baseline for calculating discounts and sale arrangements. Understanding this helps you recognize the value of discounts and sales.

An important step in solving problems like these is not just calculating a discount, but understanding what the original price implies. It ensures that the discount is calculated correctly, confirming the correct amount saved and that you're getting a genuine deal. In our exercise, the original price was given as $256, which served as the starting point for all calculations.
Recognizing and comparing the original price to both the discount amount and sale price visually illustrates the deal's value.

• Original Price: Basic point for discount calculations.
• It's key to both marketers and buyers during sales.
• Understand it thoroughly for effective budget planning.

Appreciate the original price as the anchor of all discount calculations.