Selling Price after First Discount

Oct 13, 2025 by wbrum.org 100 views

Introduction

When it comes to solving problems involving discounts and percentages, using a ratio box can be a powerful tool. A ratio box is a visual representation of the relationships between different quantities in a problem, and it can help you to organize your thinking and make calculations easier. In this article, we will use a ratio box to solve a problem involving a discount on a jacket.

The Problem

Mike paid $48 for a jacket at 25 percent off of the regular price. What was the regular price of the jacket?

Setting Up the Ratio Box

To solve this problem, we will set up a ratio box with the following quantities:

Regular Price: The original price of the jacket before the discount
Discount: The amount of the discount, which is 25 percent of the regular price
Selling Price: The price that Mike paid for the jacket, which is $48
Percent Off: The percentage of the discount, which is 25 percent

Here is the ratio box:

	Regular Price	Discount	Selling Price	Percent Off
		25%	$48	25%

Solving the Problem

To find the regular price of the jacket, we need to use the information in the ratio box to set up an equation. We know that the discount is 25 percent of the regular price, so we can write an equation:

Discount = 0.25 x Regular Price

We also know that the selling price is the regular price minus the discount, so we can write another equation:

Selling Price = Regular Price - Discount

Substituting the first equation into the second equation, we get:

Selling Price = Regular Price - 0.25 x Regular Price

Simplifying the equation, we get:

Selling Price = 0.75 x Regular Price

Now we can substitute the value of the selling price into the equation:

$48 = 0.75 x Regular Price

To solve for the regular price, we can divide both sides of the equation by 0.75:

Regular Price = $48 / 0.75

Regular Price = $64

Conclusion

Using a ratio box, we were able to solve the problem of finding the regular price of a jacket that was sold at a 25 percent discount. By setting up the ratio box and using the information in it to set up an equation, we were able to find the regular price of the jacket, which was $64.

Tips and Variations

When using a ratio box, make sure to include all of the relevant quantities in the box, including the regular price, discount, selling price, and percent off.
When setting up the equation, make sure to use the correct units and to simplify the equation as much as possible.
If the problem involves a discount that is not a percentage, you may need to use a different approach, such as using a decimal or a fraction.
If the problem involves multiple discounts or other complications, you may need to use a more complex ratio box or to break the problem down into smaller parts.

Real-World Applications

Using a ratio box to solve problems involving discounts and percentages can be useful in a variety of real-world situations, such as:

Shopping: When comparing prices and discounts at different stores
Finance: When calculating interest rates and investment returns
Business: When setting prices and calculating profits

Common Mistakes

Failing to include all of the relevant quantities in the ratio box
Failing to simplify the equation
Using the wrong units or decimal places
Failing to check the solution for reasonableness

Practice Problems

A shirt is on sale for 20 percent off of the regular price. If the selling price is $30, what is the regular price of the shirt?
A pair of shoes is discounted by 15 percent. If the selling price is $60, what is the regular price of the shoes?
A book is sold at a discount of 25 percent. If the selling price is $20, what is the regular price of the book?

Solutions to Practice Problems

A shirt is on sale for 20 percent off of the regular price. If the selling price is $30, what is the regular price of the shirt?

Set up the ratio box:

| | Regular Price | Discount | Selling Price | Percent Off | | --- | --- | --- | --- | --- | | | | 20% | $30 | 20% |

Solve the problem: Discount = 0.20 x Regular Price Selling Price = Regular Price - Discount Substituting the first equation into the second equation, we get: Selling Price = Regular Price - 0.20 x Regular Price Simplifying the equation, we get: Selling Price = 0.80 x Regular Price Substituting the value of the selling price into the equation, we get: $30 = 0.80 x Regular Price To solve for the regular price, we can divide both sides of the equation by 0.80: Regular Price = $30 / 0.80 Regular Price = $37.50

A pair of shoes is discounted by 15 percent. If the selling price is $60, what is the regular price of the shoes?

Set up the ratio box:

| | Regular Price | Discount | Selling Price | Percent Off | | --- | --- | --- | --- | --- | | | | 15% | $60 | 15% |

Solve the problem: Discount = 0.15 x Regular Price Selling Price = Regular Price - Discount Substituting the first equation into the second equation, we get: Selling Price = Regular Price - 0.15 x Regular Price Simplifying the equation, we get: Selling Price = 0.85 x Regular Price Substituting the value of the selling price into the equation, we get: $60 = 0.85 x Regular Price To solve for the regular price, we can divide both sides of the equation by 0.85: Regular Price = $60 / 0.85 Regular Price = $70.59

A book is sold at a discount of 25 percent. If the selling price is $20, what is the regular price of the book?

Set up the ratio box:

| | Regular Price | Discount | Selling Price | Percent Off | | --- | --- | --- | --- | --- | | | | 25% | $20 | 25% |

Solve the problem: Discount = 0.25 x Regular Price Selling Price = Regular Price - Discount Substituting the first equation into the second equation, we get: Selling Price = Regular Price - 0.25 x Regular Price Simplifying the equation, we get: Selling Price = 0.75 x Regular Price Substituting the value of the selling price into the equation, we get: $20 = 0.75 x Regular Price To solve for the regular price, we can divide both sides of the equation by 0.75: Regular Price = $20 / 0.75 Regular Price = $26.67

Introduction

In our previous article, we discussed how to use a ratio box to solve problems involving discounts and percentages. A ratio box is a visual representation of the relationships between different quantities in a problem, and it can help you to organize your thinking and make calculations easier. In this article, we will answer some common questions about using a ratio box to solve problems involving discounts and percentages.

Q: What is a ratio box, and how do I use it to solve problems involving discounts and percentages?

A: A ratio box is a visual representation of the relationships between different quantities in a problem. To use a ratio box to solve problems involving discounts and percentages, you need to set up the box with the following quantities:

Regular Price: The original price of the item before the discount
Discount: The amount of the discount, which is a percentage of the regular price
Selling Price: The price that the item is sold for after the discount
Percent Off: The percentage of the discount

You can then use the ratio box to set up an equation and solve for the regular price.

Q: How do I set up the ratio box?

A: To set up the ratio box, you need to include the following quantities:

Regular Price: The original price of the item before the discount
Discount: The amount of the discount, which is a percentage of the regular price
Selling Price: The price that the item is sold for after the discount
Percent Off: The percentage of the discount

You can then use the ratio box to set up an equation and solve for the regular price.

Q: What if the problem involves a discount that is not a percentage?

A: If the problem involves a discount that is not a percentage, you may need to use a different approach, such as using a decimal or a fraction. For example, if the problem involves a discount of 10 cents, you can set up the ratio box with the following quantities:

Regular Price: The original price of the item before the discount
Discount: The amount of the discount, which is 10 cents
Selling Price: The price that the item is sold for after the discount
Percent Off: The percentage of the discount (in this case, 10 cents is equivalent to 10/100 or 0.1)

Q: What if the problem involves multiple discounts or other complications?

A: If the problem involves multiple discounts or other complications, you may need to use a more complex ratio box or to break the problem down into smaller parts. For example, if the problem involves a discount of 20 percent followed by a discount of 10 percent, you can set up the ratio box with the following quantities:

Regular Price: The original price of the item before the first discount
First Discount: The amount of the first discount, which is 20 percent of the regular price
Selling Price after First Discount: The price that the item is sold for after the first discount
Second Discount: The amount of the second discount, which is 10 percent of the selling price after the first discount
Selling Price after Second Discount: The price that the item is sold for after the second discount

Q: How do I check my solution for reasonableness?

A: To check your solution for reasonableness, you need to make sure that the solution makes sense in the context of the problem. For example, if the problem involves a discount of 20 percent, you would expect the selling price to be 80 percent of the regular price. If the solution does not make sense, you may need to recheck your calculations or re-evaluate your approach.

Q: What are some common mistakes to avoid when using a ratio box to solve problems involving discounts and percentages?

A: Some common mistakes to avoid when using a ratio box to solve problems involving discounts and percentages include:

Failing to include all of the relevant quantities in the ratio box
Failing to simplify the equation
Using the wrong units or decimal places
Failing to check the solution for reasonableness

Q: How can I practice using a ratio box to solve problems involving discounts and percentages?

A: You can practice using a ratio box to solve problems involving discounts and percentages by working through examples and exercises. You can also try using a ratio box to solve real-world problems, such as calculating the cost of a purchase after a discount or determining the regular price of an item based on its selling price.

Q: What are some real-world applications of using a ratio box to solve problems involving discounts and percentages?

A: Some real-world applications of using a ratio box to solve problems involving discounts and percentages include:

Shopping: When comparing prices and discounts at different stores
Finance: When calculating interest rates and investment returns
Business: When setting prices and calculating profits

Q: How can I use a ratio box to solve problems involving other types of percentages, such as sales tax or tips?

A: You can use a ratio box to solve problems involving other types of percentages, such as sales tax or tips, by setting up the ratio box with the following quantities:

Original Price: The original price of the item before the tax or tip
Tax or Tip: The amount of the tax or tip, which is a percentage of the original price
Final Price: The price that the item is sold for after the tax or tip

You can then use the ratio box to set up an equation and solve for the final price.

Q: What are some common types of problems that involve discounts and percentages?

A: Some common types of problems that involve discounts and percentages include:

Calculating the cost of a purchase after a discount
Determining the regular price of an item based on its selling price
Comparing prices and discounts at different stores
Calculating interest rates and investment returns
Setting prices and calculating profits

Q: How can I use a ratio box to solve problems involving multiple discounts or other complications?

A: You can use a ratio box to solve problems involving multiple discounts or other complications by setting up the ratio box with the following quantities:

Regular Price: The original price of the item before the first discount
First Discount: The amount of the first discount, which is a percentage of the regular price
Selling Price after First Discount: The price that the item is sold for after the first discount
Second Discount: The amount of the second discount, which is a percentage of the selling price after the first discount
Selling Price after Second Discount: The price that the item is sold for after the second discount

You can then use the ratio box to set up an equation and solve for the selling price after the second discount.

Q: What are some tips for using a ratio box to solve problems involving discounts and percentages?

A: Some tips for using a ratio box to solve problems involving discounts and percentages include:

Make sure to include all of the relevant quantities in the ratio box
Simplify the equation as much as possible
Use the correct units and decimal places
Check the solution for reasonableness
Practice using a ratio box to solve problems involving discounts and percentages

Q: How can I use a ratio box to solve problems involving other types of percentages, such as sales tax or tips?

A: You can use a ratio box to solve problems involving other types of percentages, such as sales tax or tips, by setting up the ratio box with the following quantities:

Original Price: The original price of the item before the tax or tip
Tax or Tip: The amount of the tax or tip, which is a percentage of the original price
Final Price: The price that the item is sold for after the tax or tip

You can then use the ratio box to set up an equation and solve for the final price.

Q: What are some common mistakes to avoid when using a ratio box to solve problems involving discounts and percentages?

A: Some common mistakes to avoid when using a ratio box to solve problems involving discounts and percentages include:

Failing to include all of the relevant quantities in the ratio box
Failing to simplify the equation
Using the wrong units or decimal places
Failing to check the solution for reasonableness

Q: How can I practice using a ratio box to solve problems involving discounts and percentages?

Q: What are some real-world applications of using a ratio box to solve problems involving discounts and percentages?

A: Some real-world applications of using a ratio box to solve problems involving discounts and percentages include:

Shopping: When comparing prices and discounts at different stores
Finance: When calculating interest rates and investment returns
Business: When setting prices and calculating profits

Q: How can I use a ratio box to solve problems involving other types of percentages, such as sales tax or tips?

A: You can use a ratio box to solve problems involving other types of percentages, such as sales tax or tips, by setting up the ratio box with the following quantities:

Original Price: The original price of the item before the tax or tip
Tax or Tip: The amount of the tax or tip, which is a percentage of the original price
Final Price: The price that the item is sold for after the tax or tip

You can then use the ratio box to set up an equation and