Problem 44 - Prealgebra

Question

Aiden wants to buy a tent that costs \(\$ 150\) for his camping trip. The tent is on sale at a \(30 \%\) discount. What will be the sale price of the tent?A \(\$ 45\) C \(\$ 105\) B \$95 D \(\$ 110\)

Step-by-Step Solution

Answer

The sale price is $105.

Step 1: Understand the Discount Percentage

The tent costs $150, and it's being sold at a 30% discount. This means that the price will be reduced by 30% of its original cost.

Step 2: Calculate the Discount Amount

To find the discount amount, calculate 30% of the original price: \[ Discount = 0.30 \times 150 = 45 \] This means the tent will be discounted by $45.

Step 3: Calculate the Sale Price

Subtract the discount amount from the original price to find the sale price: \[ Sale\ Price = 150 - 45 = 105 \] Thus, the sale price of the tent is $105.

Key Concepts

Understanding Discount Calculation

When it comes to discount calculation, it is essential to grasp the concept of percentage. A discount represents a reduction from the original price. It's usually expressed as a percentage to make it easier to understand how much you'll save.
In this context, a 30% discount on a tent signifies that the price will be reduced by a portion that is equivalent to 30% of the original price. When calculating how much to subtract from the original cost, convert the percentage into a decimal form. In this case, 30% is equivalent to 0.30. So, the discount can be calculated by multiplying this decimal by the original tent price. This is a straightforward multiplication:

• Convert percentage to decimal: 30% = 0.30
• Calculate discount amount: $150 × 0.30 = $45

Understanding this basic arithmetic will allow you to determine how much money you can save through discounts on various purchases.

Sale Price Simplified

Finding out the sale price after applying a discount is an essential skill. Once you know the discount amount, determining the sale price involves a simple subtraction. Subtract the discount value from the original price to determine the price you'll actually pay. This is how you can ensure you're paying the right amount at a sale.
For Aiden's tent, the original price was $150, and we calculated a discount of $45. To find the sale price after the discount, follow these steps:

• Original Price: $150
• Discount Amount: $45
• Subtract Discount from Original Price: $150 - $45 = $105

Thus, the sale price of the tent, after applying the discount, is $105. This efficient method helps you make smart buying decisions during sales.

Basic Arithmetic in Everyday Shopping

Basic arithmetic skills are invaluable, especially during shopping. They come into play when calculating discounts, sale prices, and more. With these skills, you can understand and perform calculations effortlessly and with confidence.
To tackle such problems, always start with converting percentages to decimals. This conversion is pivotal in computing the discount amount accurately. Then, to determine the final price, use straightforward subtraction. Mastering these calculations not only applies to finding sale prices but is also useful in budgeting, comparing deals, and avoiding overspending.
Whether you're planning a camping trip like Aiden or shopping for daily groceries, knowing how to do these simple arithmetic calculations can save you money and bring clarity to your shopping experience. Practice makes perfect, so apply these skills to real-world scenarios regularly.