Problem 218 - Prealgebra

Question

In the following exercises, solve. Shopping A mattress set is on sale for \(\$ 755 .\) Its regular price is \(\$ 1,600\) . What is the difference between the regular price and the sale price?

Step-by-Step Solution

Answer

The difference is \( \$ 845 \).

Step 1: Understand the Problem

Identify the regular price and the sale price. The regular price of the mattress set is \( \$ 1600 \) and the sale price is \( \$ 755 \).

Step 2: Set Up the Equation

To find the difference between the regular price and the sale price, subtract the sale price from the regular price: \( \text{Difference} = \text{Regular Price} - \text{Sale Price} \).

Step 3: Perform the Calculation

Subtract \( \$ 755 \) from \( \$ 1600 \): \( \$ 1600 - \$ 755 = \$ 845 \).

Step 4: Interpret the Result

The difference between the regular price and the sale price is \( \$ 845 \).

Key Concepts

problem-solving steps

When solving any word problem, following a step-by-step approach can make the process much easier.

• Step 1: Understand the Problem - Know what you need to find and identify the given data.
• Step 2: Set Up the Equation - Translate the word problem into a mathematical equation.
• Step 3: Perform the Calculation - Execute the calculations accurately.
• Step 4: Interpret the Result - Provide a clear and understandable answer to the problem.

Let's apply these steps to our mattress problem. We start by understanding that we need to find out how much money is saved by purchasing the mattress on sale. Setting up the equation, we will subtract the sale price from the regular price. Then, we carry out the subtraction to get our final result.

subtraction

Subtraction is a basic arithmetic operation that represents the operation of removing objects from a collection.

In this exercise, we use subtraction to find the difference between the regular price and the sale price of a mattress set. Subtraction helps us to compare two numbers and determine how much more or less one quantity is from another.

The equation set up for the problem is:

\[\text{Difference} = \text{Regular Price} - \text{Sale Price}\]

Subtracting the sale price of \(\text{\textdollar}755\) from the regular price of \(\text{\textdollar}1600\), we find the difference:

\[\text{\textdollar} 1600 - \text{\textdollar} 755 = \text{\textdollar} 845\]

Thus, the difference is \(\text{\textdollar} 845\).

real-life math applications

Mathematics is not just a subject you learn in school; it has real-life applications in everyday situations.

Buying a mattress on sale, as illustrated in our exercise, is a perfect example.

Understanding how to calculate the difference between sale and regular prices helps you make informed purchasing decisions.

Here are some other scenarios where these skills are applicable:

• Budgeting and managing expenses
• Calculating discounts while shopping
• Comparing prices of different products

By applying basic arithmetic operations like subtraction in these real-life contexts, we can efficiently handle financial transactions and save money.

basic arithmetic

Basic arithmetic includes the fundamental operations: addition, subtraction, multiplication, and division. These are the building blocks for all math concepts.

In our mattress example, we primarily used subtraction to solve the problem.

To recap:

• Addition combines quantities together.
• Subtraction determines the difference between quantities.
• Multiplication is repeated addition of the same number.
• Division splits a quantity into equal parts.

Mastering these basic operations is crucial. They enable you to solve everyday problems related to shopping, budgeting, and more. Whether you're calculating how much you've saved during a sale or splitting a bill, these operations are essential tools in your mathematics toolkit.