## What Does Discount Mean in Math?

**Discount (typically represented as a percentage) is a promotional or marketing strategy that refers to a reduction from the original price of an item or a service offered by a store or a company to attract more customers.**

Let’s say your favorite toy costs $\$10$, but the store offers a 20% discount on it. This means that the store is taking 20% off the original price to make it cheaper for you. After applying the discount, you will pay only $\$8$, less than the original price of the toy.

A discount is offered for various reasons, such as to encourage sales, to clear out old stock or inventory, to promote new products or services offered by the store, to attract new customers, and boost customer retention, etc.

Before we go into further detail, let’s quickly revise a few technical terms we use when calculating discounts.

**Cost Price:**The original price at which a product or an item is purchased by a business or an individual.**Marked Price/List Price:**The price at which a product is listed or labeled for sale by the seller before any discounts or price reductions.**Selling Price:**The final price at which a product or item is sold to a customer after discounts or price reductions have been applied.

## Discount Definition

**A discount is a reduction or deduction from the original price of a product or service, allowing customers to pay less than the original or regular price.**

The discount can be expressed as a **percentage** or a **specific amount**.

## Types of Discounts

In simple terms, trade discounts are for businesses buying in bulk, quantity discounts are for customers buying more of a product, and promotional discounts are temporary offers to attract customers. These discounts make shopping more affordable and provide incentives for customers and businesses to make purchases.

**Trade Discounts:**Trade discounts are special price reductions given by manufacturers or wholesalers to retailers or distributors. It’s like a “wholesale” price that encourages retailers to buy in larger quantities. This discount is not applicable to the customers.

**Quantity Discounts:**Quantity discounts are discounts offered when you buy a product in bulk or in a large quantity. The more you buy, the lower the price per item. It’s like a “bulk” discount where you get a better deal for purchasing a larger quantity.

**Promotional Discounts:**Promotional discounts are special offers or sales events. They can include percentage discounts, buy-one-get-one (BOGO) deals, or free shipping offers. These discounts usually last for a limited time to create excitement and encourage customers to make a purchase.

## Discount Formula

The discount calculation can be done in two cases:

**Case 1: When both the list price and selling price are given**

In this case, the discount can be calculated by subtracting the selling price from the list price.

The following are the formulas we use to calculate discounts:

**Discount amount = List Price – Selling Price**

Two formulas can be derived from the above formula.

- Selling price = List Price – Discount amount

- List Price = Selling Price + Discount amount

**Case 2: When the discount percentage is given**

In this case, the discount amount can be calculated by multiplying the discount percentage by the list price divided by 100.

**Discount amount = **$\frac{Discount %}{100} \times $** List Price**

## How to Calculate Discount

**Case 1: When both the list price and selling price are given**

When both the list price and selling price are given, we calculate discount using the formula:

**Discount = List Price ****–**** Selling Price**

Let’s understand the steps with the help of an example. If a pair of shoes has a list price of $80 and are being sold for $65 during a sale, what is the discount?

**Step 1:** Note down the list price and selling price.

List price $= \$80$

Selling price $= \$65$

**Step 2: **Plug in the given values in the formula and calculate the discount.

Discount = List Price – Selling Price

Discount $= \$80 \;-\; \$65$

Discount $= \$15$

Therefore, the discount on the pair of shoes is $\$15$.

**Case 2: When the discount percentage is given**

There are two methods to calculate the discount amount when the discount percentage is given.

Lets understand both the methods with the help of an example. If the list price of a product is $\$200$ and the store offers a 20% discount, what is the selling price?

**Step 1:** Note down the list price and the discount percentage.

List price$ = \$200$

Discount percentage = 20%

**Step 2:** Note down the formula.

Discount $= \frac{Discount %}{100}\times$ List Price

**Step 3:** Substitute the values and calculate the discount amount.

Discount amount $= \frac{20}{100} \times 200 = 20 \times 2 = 40$

**Step 4:** Subtract the discount amount from the list price to obtain the selling price.

S.P. = L.P. – Discount

$\$200 \;-\; \$40 = \$160$.

Therefore, the selling price after a 20% discount is $160.

There’s another way to solve this one.

**Step 1: **Convert the discount percentage into a decimal.

20% $= \frac{20}{100} = 0.2$.

**Step 2: **Multiply the list price by the decimal to find the discount amount.

$0.2 \times \$200 = \$40$

Discount $= \$40$

**Step 3:** Subtract the discount amount from the list price to obtain the selling price:

Selling price $= \$200 \;-\; \$40 = \$160$.

Therefore, the selling price after a 20% discount is $\$160$.

## What Is Discount Rate?

**The discount rate refers to the percentage by which the price of an item has been reduced.**

It is calculated by taking the difference between the list price (original price) and the selling price (discounted price), dividing it by the list price, and multiplying by 100 to express it as a percentage.

The discount percentage formula is given as:

**Discount Rate (%) **$= \frac{(List\; Price\; – \;Selling\; Price)}{List \;Price} \times 100$

Alternatively, it can also be calculated using the formula:

**Discount Rate (%) **$= \frac{Discount \;Amount}{List\; Price}\times 100$

The discount rate helps customers understand the magnitude of the price reduction and compare different discount offers. It is a useful measure for evaluating the savings achieved through a discount.

## How to Find the Discounts Rate in Math

To calculate the discount rate, you need to know the original price (list price) and the discounted price (selling price), or you need to know the discount.

**Example: **An item originally priced at $100 is on sale for $80. Calculate the discount rate.

**Solution: **

List Price $= \$100$

Selling Price $= \$80$

Using the formula:

Discount Rate (%) $= \frac{(List\; Price \;- \;Selling \;Price)}{List\; Price}\times 100$

Discount Rate (%) $= \frac{\$100 \;-\; \$80}{\$100} \times 100$

Discount Rate (%) $= \frac{\$20}{\$100} \times 100$

Discount Rate (%) = 20%

So, in this case, the discount rate is 20%. It indicates that the item has been discounted by 20% off the original price.

## Facts on Discounts

- A discount is a reduction in the price of an item or service.
- The discount amount can be calculated by subtracting the discounted price (selling price) from the original price.
- The discount rate is the percentage by which the price has been reduced.
- As the discount rate increases, the discount amount increases and ultimately the discounted price (selling price) decreases.

## Conclusion

In this article, we have learned about discounts and how it is calculated. Understanding discounts in math is important for making informed purchasing decisions, evaluating savings, and solving various mathematical problems related to pricing and discounts. Now, let’s solve some discount examples and practice problems to understand the concept better.

## Solved Examples on Discounts

**1. Jane has a coupon that gives a 25% discount on any item in the store. If she buys a $200 item, how much money will she save with the coupon?**

**Solution: **

Discount percent = 25%

List price$ = \$200$

Discount $= \frac{Discount %}{100}\times$ List Price

Discount $= \frac{25}{100} \times 200$

Discount $= 25 \times 2 = 50$

Therefore, Jane will save $\$50$ with the coupon.

**2. The list price of a smartphone is **$\$800$**, and it is sold for **$\$640$**. Calculate the discount rate percentage.**

**Solution:**

List price $= \$800$

Selling Price $= \$640$

Discount Rate Formula (%) $= \frac{List\; Price \;-\; Selling \;Price}{List\; Price} \times 100$

Discount Rate (%) $= \frac{800 \;-\; 640}{800} \times 100$

Discount Rate (%) $= \frac{160}{800} \times 100$

Discount Rate (%) $= \frac{160}{8}$

Discount Rate (%) = 20%

Therefore, the discount rate percentage for the smartphone is 20%.

**3. A department store has a sale with a discount of 40% on all clothing items. If Mark bought a shirt for **$\$25$** and a pair of jeans for **$\$40$**, what was the total discount he got?**

**Solution: **

Total purchase $= \$25 + \$40 = \$65$

Discount = 40%

Discount amount $= \$65 \times \frac{40}{100} = \$26$

Therefore, Mark received a total discount of $\$26$ on his purchases.

Note that if you calculate the discount separately and then add them together, the answer will be the same.

Discount on the shirt = 40% of $\$25 = \$10$

Discount on the pair of jeans = 40% of $\$40 = \$16$

Total discount $= \$10 + \$16 = \$26$

## Practice Problems on Discounts

## Discounts: Definition, Formula, Rate, Solved Examples, Facts

### What does the term "list price" refer to in the context of discounts?

The list price is the initial price of a product or service, typically set by the retailer or manufacturer.

### A $\$100$ watch is sold at a 11% discount. What is its selling price?

Discount = 11% of $\$100 = \$11$

Selling price = $\$100 \;-\; \$11 = \$89$

### Which formula is used to calculate the discount amount?

The discount amount is calculated by subtracting the selling price from the list price.

### Which formula is used to calculate the discount rate?

Discount Rate (%) $= \frac{(List\; Price \;-\; Selling Price)}{List \;Price} \times 100} = \frac{Discount \;Amount}{List\; Price}\times 100$

### What is the discount amount if a $\$65$ item was purchased for $\$49$?

Discount amount = Selling price - List price $= \$65 \;-\; \$49 = \$16$

## Frequently Asked Questions on Discounts

**Why do businesses offer discounts?**

Businesses offer discounts to attract customers, increase sales volume, clear out inventory, promote new products, reward customer loyalty, or run special promotions.

**Are discounts always beneficial for customers?**

Discounts can be beneficial for customers as they provide cost savings. However, customers should also consider the quality, value, and need for the product or service before making a purchase solely based on the discount.

**What is the difference between a discount and a sale?**

A discount is a reduction in price offered on specific products or services, whereas a sale refers to a broader event where multiple items are marked down or special promotions are available.

**What is a fixed discount?**

A fixed discount is a specific amount subtracted from the original price. It does not depend on the list price of an item. It remains the same.

**What is the difference between a discount and a rebate?**

A discount is a reduction in price, while a rebate is a refund after purchase. A discount is applied to the initial price, whereas a rebate involves receiving a partial refund after completing a purchase.

**How do you calculate the savings from a discount?**

To calculate the savings from a discount, subtract the discounted price from the original price. Savings = Original Price – Discounted Price.