Problem 97 - Introductory and Intermediate Algebra for College Students 4th

Question

Will help you prepare for the material covered in the next section. In each exercise, write an integer that is the result of the given situation. You earn \(\$ 150\), but then you misplace \(\$ 90\).

Step-by-Step Solution

Answer

The final remaining amount is \$60

Step 1: Establish The Initial Amount

The initial amount that is earned is $150. This value is the start point for any further calculations.

Step 2: Factor In The Loss

Out of this $150, $90 is misplaced or lost. To find out the remaining amount, this loss needs to be subtracted from the initial sum.

Step 3: Perform The Subtraction

The subtraction operation is done as follows: 150 - 90. This will give the remaining amount after the loss.

Key Concepts

Subtraction in Math

Subtraction is a fundamental arithmetic operation that allows us to find the difference between two numbers or quantities. It involves taking away a certain amount from a larger number to find what remains. Subtraction is represented by the minus sign (-), and it answers questions like, "How many are left?" or "How much is missing?"

In the example exercise, we started with $150. When $90 is misplaced, we need to determine how much money is left. We perform the subtraction operation: 150 - 90. This simply means removing 90 from the 150 we originally had.

• The number from which we subtract (150 in this case) is called the minuend.
• The number we subtract (90 in this example) is the subtrahend.
• The result or outcome (60 here) is termed the difference.

Subtraction helps us quantify the remaining amount after a loss, as seen in various scenarios involving money, items, or any measurable quantities.

Applying Math to Real-World Scenarios

Mathematics is an essential tool for navigating everyday life, and real-world math problems are practical applications of mathematical principles in daily activities. Whether shopping, budgeting, or planning a trip, mathematics helps us make informed decisions.

In the given exercise, the scenario of earning and then misplacing money is a realistic situation many might face. This highlights how understanding basic operations, such as subtraction, can help in:

• Resolving financial discrepancies by knowing how much money is left.
• Budgeting expenses to ensure funds are spent wisely.
• Understanding the impact of losses or mistakes on overall balance.

Being able to frame mathematical problems in the context of everyday life not only enhances problem-solving skills but also gives mathematics a relatable, tangible significance.

Grasping Basic Arithmetic

Basic arithmetic encompasses the four fundamental operations: addition, subtraction, multiplication, and division. These operations form the foundation of mathematics and are crucial for solving simple to complex mathematical problems.

Understanding arithmetic is important because it:

• Enables us to perform calculations quickly and accurately.
• Lays the groundwork for more advanced mathematical concepts and operations.
• Helps in decision-making and planning in daily activities.

In the example problem, subtraction is the arithmetic operation used to determine the remaining amount of money after losing a portion of it. Mastering basic arithmetic ensures that you can handle a variety of tasks, from calculating change during purchases to managing personal finances. Starting with these foundational skills leads to greater confidence and efficiency in mathematical reasoning.