Question

If the sale price on a coat is \(\$ 72\) and the original price of the coat was \(\$ 90\), what is the percent discount from this sale? (A) \(14 \%\) (B) \(20 \%\) (C) \(26 \%\) (D) \(80 \%\)

Short answer

The percent discount is 20%.

Step-by-step solution

Calculate the Discount Amount

To find the discount amount, subtract the sale price from the original price. Original price: \(\\(90\), Sale price: \(\\)72\). Discount amount: \(\\(90 - \\)72 = \$18\).

Determine the Discount Percentage

To find the discount percentage, divide the discount amount by the original price, then multiply the result by 100 to convert it to a percentage. The formula is: \(\frac{\text{Discount amount}}{\text{Original price}} \times 100\). Substitute the values: \(\frac{18}{90} \times 100\).

Perform the Calculations

Calculate \(\frac{18}{90} = 0.2\). Multiply by 100: \(0.2 \times 100 = 20\%\).

Compare with Given Options

The calculated discount percentage is \(20\%\). Refer to the given options and match the calculated discount percentage to option (B): \(20\%\).

Key concepts

Discount Calculation Made Easy

Discount calculation is a valuable skill that allows you to determine how much you save when making a purchase during a sale. Understanding this concept involves a few straightforward steps. First, identify the original price and the sale price of the item you are purchasing. The difference between these two prices is the discount amount. In other words, you subtract the sale price from the original price.

Let's break it down:

• Original Price: The starting price before any reductions. For example, the coat costs \(90 originally.
• Sale Price: The price you're asked to pay during the sale, e.g., \)72 for the coat.
• Discount Amount: This is calculated by subtracting the sale price from the original price: \(90 - \)72 = $18.

To find out the percentage of the discount, divide the discount amount by the original price and multiply the result by 100. This conversion to percentage is key since it tells you what portion of the original price you're not paying.

Hence, the formula:\[\text{Discount Percentage} = \left(\frac{\text{Discount Amount}}{\text{Original Price}}\right) \times 100\]In the coat example, you would calculate:\[\frac{18}{90} \times 100 = 20\%\]This means you are enjoying a 20% discount on the original price.

Mastering Problem Solving with Percentages

Problem-solving is at the heart of mathematics, and working with percentages is a common problem-solving scenario. Start by understanding what the problem is asking. Often, it could involve finding percentage discounts, like in our example.

When approaching problems:

• Identify what you know: the original and sale prices.
• Determine what you need to find: the percentage discount.
• Use the formula for discount calculation as a point of reference.

Massaging the problem into familiar calculation steps aids clarity. Always remember to align your answer with the context of the problem. For example, in retail, the relevance of a percentage discount helps in understanding the value of the deal you're getting.

Approach each step methodically:

• Subtract to find the discount amount.
• Calculate the discount percentage using the formula.
• Consider other information provided, such as multiple-choice answers, to cross-check your solution.
• Reflect on your answer to ensure it makes logical sense in the context of the problem.

This structured approach demystifies percentage problems and enhances your confidence in tackling similar questions.

Tackling PSAT Math with Confidence

The PSAT math section is designed to test your ability to apply mathematical concepts in practical situations. Understanding how to handle percentage questions, such as discount calculations, is a practical skill emphasized in these tests.

To excel in PSAT math:

• An understanding of key math concepts like percentages, ratios, and simple algebra is crucial.
• Practice problems regularly to build familiarity and speed.
• Break down questions into manageable parts so you're not overwhelmed.

A real-world context, such as calculating the percentage discount, is typical in the PSAT question pool, allowing you to see the application of math in everyday life. By understanding the basics—like knowing how to find the difference in prices and converting that into a percentage—you'll be able to handle other math problems confidently.

As you practice problems like these:

• Focus on precision in arithmetic and conversion practices.
• Use process of elimination in multiple-choice settings to narrow down options.
• Reflect on errors to prevent repeating them in future exercises.

By integrating these strategies, you're well-prepared to tackle the PSAT math section thoughtfully, using logic and structured problem-solving honed through practice.