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# Discount, Tax, And Tip Word Problems

## Introduction

Discount, taxes, and tip are common concepts encountered in financial transactions, especially in the context of purchasing goods or services. Here’s a brief explanation of each:

### Discount

A discount is a reduction in the price of an item or service. It is often expressed as a percentage of the original price. Discounts can be offered for various reasons, such as promotional sales, loyalty programs, or bulk purchases. For example, if an item originally costs \$100 and there’s a 20% discount, the discounted price would be \$80.

### Tax

Tax is an additional amount of money imposed by the government on goods and services, typically calculated as a percentage of the purchase price. The tax rate varies depending on the jurisdiction and the type of goods or services being purchased. Sales tax is a common form of tax applied to retail purchases. For example, if a product costs \$50 and the sales tax rate is 10%, the total cost including tax would be \$55.

### Tip

A tip, also known as a gratuity, is an extra amount of money given voluntarily to someone who provides a service, such as a waiter in a restaurant or a taxi driver. Tips are usually calculated as a percentage of the total bill. The customary tip rate can vary depending on cultural norms and the quality of service received. For example, if a restaurant bill totals \$80 and the customary tip rate is 15%, the tip would be \$12.

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## Example Questions

1. Problem on Discount:

A store is offering a 20% discount on all its items. If a dress originally costs \$50, how much will it cost after the discount?

Solution

Given that the dress originally costs \$50 and there’s a 20% discount, we can find the discounted price by multiplying the original price by the fraction representing the discount (1 – 0.20 = 0.80):

Discounted price = \$50 x 0.8 = \$40

So, the dress will cost \$40 after the discount.

2. Problem on Tax:

If a laptop costs \$1000 and the sales tax rate is 8%, how much will you pay in total including tax?

Solution

To find the total cost including tax, we need to add the original cost to the tax amount. The tax amount can be calculated by multiplying the original cost by the tax rate (0.08):

Tax = \$1000 x 0.08 = \$80

Adding this tax amount to the original cost gives the total cost:

Total cost = \$1000 + \$80 = \$1080

So, you will pay \$1080 in total including tax.

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3) Problem on Tip:

If you had a meal at a restaurant that costs \$40 and you wanted to leave a 15% tip, how much tip would you leave?

Solution:

To find the tip amount, we multiply the original cost of the meal by the tip percentage (0.15):

Tip = \$40 x 0.15 = \$6

So, you will leave a \$6 tip.

4. Problem on Discount and Tax:

A pair of shoes originally cost \$80, but there’s a 10% discount on them. If the sales tax rate is 7% on the discounted price, how much will you pay in total, including tax, after the discount?

Solution:

First, we find the discounted price of the shoes:

Discounted Price = \$80 x 0.90 = \$72

Then, we calculate the tax amount on the discounted price:

Tax = \$72 x 0.07 = \$5.04

Finally, we add the discounted price and the tax amount to find the total cost:

Total Cost = \$72 + \$5.04 = \$77.04

So, you will pay \$77.04 in total, including tax, after the discount.

## Discount, Tax, And Tip FAQS

#### What is a discount?

A discount is a reduction in the price of an item or service. It is often expressed as a percentage of the original price.

#### How do you calculate the amount of discount?

To calculate the amount of discount, multiply the original price by the discount rate (in decimal form). The discount amount is then subtracted from the original price.

#### What is sales tax?

Sales tax is a percentage of the purchase price of an item or service that is added to the total cost at the point of sale. It is collected by the government and varies by location.

#### How do you calculate the total cost including tax?

To calculate the total cost including tax, add the sales tax amount to the original price of the item or service.

#### What is a tip?

A tip, also known as a gratuity, is an additional amount of money given voluntarily to someone who provides a service, such as a waiter or hairstylist.

#### How do you calculate the tip amount?

To calculate the tip amount, multiply the total bill by the tip percentage (in decimal form).

#### What is the total amount paid when considering both tax and tip?

The total amount paid when considering both tax and tip is the sum of the original price, the sales tax amount, and the tip amount.

#### How do you calculate the final price after discount, tax, and tip?

To calculate the final price after discount, tax, and tip, subtract the discount amount from the original price, then add the sales tax amount, and finally add the tip amount.

#### What is the difference between discount, tax, and tip?

A discount reduces the original price of an item, while tax and tip increase the total cost. Tax is mandatory and imposed by the government, while tip is voluntary and given as a token of appreciation for service.

#### What are some real-life scenarios where discount, tax, and tip problems are encountered?

Discount, tax, and tip problems are encountered in various real-life scenarios such as shopping, dining at restaurants, getting services like hairstyling or car maintenance, and booking travel accommodations.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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