discount

What is discount in math? Definition

In mathematics, a discount refers to a reduction in the original price of a product or service. It is commonly used in the context of sales, promotions, or special offers, where the seller offers a lower price to attract customers. The discount is usually expressed as a percentage or a fixed amount subtracted from the original price.

History of discount

The concept of discounts has been around for centuries, with evidence of its use dating back to ancient civilizations. In ancient Rome, for example, merchants would offer discounts to soldiers as a way to boost sales and show appreciation for their service. Over time, the practice of offering discounts has evolved and become a common marketing strategy used by businesses worldwide.

What grade level is discount for?

The concept of discounts is typically introduced in elementary or middle school mathematics, around grades 4-7. It is a fundamental concept that helps students understand the relationship between original prices, discounts, and final prices. As students progress to higher grade levels, they may encounter more complex discount problems involving multiple discounts or compound interest.

What knowledge points does discount contain? And detailed explanation step by step

The concept of discount involves several key knowledge points, including:

1. Original price: The initial price of a product or service before any discount is applied.
2. Discount rate: The percentage or fixed amount by which the original price is reduced.
3. Discounted price: The final price after the discount has been applied.

To calculate the discounted price, follow these steps:

1. Determine the original price of the item.
2. Identify the discount rate or amount.
3. Calculate the discount by multiplying the original price by the discount rate (if it's a percentage) or subtracting the discount amount (if it's a fixed amount).
4. Subtract the discount from the original price to find the discounted price.

For example, if a shirt originally costs $50 and is on sale for 20% off, the discount would be $50 * 0.20 = $10. The discounted price would then be $50 - $10 = $40.

Types of discount

There are several types of discounts commonly used:

1. Percentage discount: This type of discount is expressed as a percentage of the original price. For example, a 20% discount means the price is reduced by 20% of the original price.
2. Fixed amount discount: In this type of discount, a specific amount is subtracted from the original price. For example, a $10 discount means $10 is deducted from the original price.
3. Buy one, get one free (BOGO): This type of discount offers customers a free item when they purchase one at the regular price.
4. Volume discount: Businesses often offer volume discounts to customers who purchase large quantities of a product. The discount increases as the quantity purchased increases.

Properties of discount

Some properties of discounts include:

1. Discounts are always subtracted from the original price.
2. The discounted price is always lower than the original price.
3. Discounts can be applied to individual items or the total purchase amount.
4. Multiple discounts can be applied sequentially to further reduce the price.

How to find or calculate discount?

To find or calculate the discount, follow these steps:

1. Determine the original price.
2. Identify the discount rate or amount.
3. Calculate the discount by multiplying the original price by the discount rate (if it's a percentage) or subtracting the discount amount (if it's a fixed amount).

What is the formula or equation for discount?

The formula for calculating the discount is:

Discount = Original Price * Discount Rate

Where:

• Discount is the amount of money or percentage reduced from the original price.
• Original Price is the initial price of the product or service.
• Discount Rate is the percentage or fixed amount of the discount.

How to apply the discount formula or equation?

To apply the discount formula, substitute the values of the original price and discount rate into the equation and calculate the discount. Then, subtract the discount from the original price to find the discounted price.

For example, if the original price is $100 and the discount rate is 20%, the discount would be $100 * 0.20 = $20. The discounted price would then be $100 - $20 = $80.

What is the symbol or abbreviation for discount?

The symbol commonly used to represent a discount is "%", which stands for percentage. It is often placed after the discount rate to indicate that it is a percentage reduction.

What are the methods for discount?

There are various methods for applying discounts, depending on the context and purpose. Some common methods include:

1. Percentage discounts: This method involves reducing the original price by a certain percentage.
2. Fixed amount discounts: In this method, a specific amount is subtracted from the original price.
3. Coupon codes: Online retailers often provide customers with coupon codes that can be entered during checkout to apply a discount.
4. Seasonal sales: Businesses may offer discounts during specific seasons or holidays to attract customers.
5. Loyalty programs: Some businesses offer discounts to loyal customers as a reward for their continued patronage.

More than 3 solved examples on discount

Example 1: A pair of shoes originally costs $80. They are on sale for 25% off. What is the discounted price?

Solution: Discount = $80 * 0.25 = $20 Discounted price = $80 - $20 = $60

Example 2: A store offers a buy one, get one free (BOGO) deal on shirts. If the original price of a shirt is $30, how much would two shirts cost?

Solution: Since it's a BOGO deal, the price of one shirt is halved. Discounted price per shirt = $30 / 2 = $15 Total cost for two shirts = $15 + $15 = $30

Example 3: A store offers a volume discount on laptops. If the original price of a laptop is $1000 and the discount rate is 10% for purchasing 5 or more laptops, how much would it cost to buy 6 laptops?

Solution: Discount = $1000 * 0.10 = $100 Discounted price per laptop = $1000 - $100 = $900 Total cost for 6 laptops = $900 * 6 = $5400

Practice Problems on discount

1. A shirt originally costs $40. It is on sale for 30% off. What is the discounted price?
2. A store offers a fixed amount discount of $15 on a pair of jeans. If the original price is $60, what is the discounted price?
3. A bookstore offers a 20% discount on all books. If the original price of a book is $25, what is the discounted price?
4. A store offers a buy two, get one free (BOGO) deal on socks. If the original price of a pair of socks is $10, how much would three pairs cost?
5. A store offers a volume discount on smartphones. If the original price of a smartphone is $500 and the discount rate is 15% for purchasing 3 or more smartphones, how much would it cost to buy 4 smartphones?

FAQ on discount

Question: What is a discount? Answer: A discount is a reduction in the original price of a product or service.

Question: How is a discount calculated? Answer: A discount can be calculated by multiplying the original price by the discount rate (if it's a percentage) or subtracting the discount amount (if it's a fixed amount).

Question: Can multiple discounts be applied? Answer: Yes, multiple discounts can be applied sequentially to further reduce the price.

Question: What are some common types of discounts? Answer: Some common types of discounts include percentage discounts, fixed amount discounts, buy one, get one free (BOGO) deals, and volume discounts.

Question: How is a discount represented? Answer: The symbol commonly used to represent a discount is "%", which stands for percentage. It is often placed after the discount rate to indicate that it is a percentage reduction.