Problem 54 - College Algebra

Question

For the following exercises, consider this scenario: Fred earns \(\$ 40\) mowing lawns. He spends \(\$ 10\) on mp3s, puts half of what is left tin a savings account, and gets another \(\$ 5\) for washing his neighbor's car. How much money does Fred keep?

Step-by-Step Solution

Answer

Fred keeps $20.

Step 1: Determine Initial Earnings

Fred earns an initial amount of $40 by mowing lawns. This is the starting point for his finances.

Step 2: Subtract Expenses

Fred spends $10 on mp3s. Subtract this from his initial earnings: $40 - $10 = $30. He now has $30 left.

Step 3: Calculate Savings Deposit

Fred puts half of the remaining $30 into a savings account. Divide the remaining money by 2: $30 / 2 = $15. He deposits $15 into his savings account.

Step 4: Calculate Remaining Money

After saving, Fred still has $15 left from his expenses and savings deduction.

Step 5: Add Additional Earnings

Fred earns an additional $5 by washing his neighbor's car. Add this to the remaining amount: $15 + $5 = $20.

Key Concepts

Financial Mathematics

Financial mathematics deals with practical problems related to finances, involving operations like earning, spending, and saving money. By understanding financial mathematics, you can better manage your money in real-life scenarios like budgets and savings. In this exercise, Fred has to allocate and manage his earnings effectively:

• He starts with earning money from mowing lawns and washing cars.
• He allocates money for leisure activities and saving.

Through these actions, Fred demonstrates key principles of financial mathematics, which focus on managing earnings and expenses smartly. Understanding this concept can help you apply similar strategies to manage your finances effectively and encourage saving habits by depositing a portion of your earnings.

Step-by-step Solutions

A step-by-step solution is crucial for comprehending and solving complex problems. It allows you to break down a problem into smaller, more manageable parts, making the solution easier to follow and understand. In Fred's financial scenario, the step-by-step approach was as follows:

• Step 1: Establish Fred's total initial income from mowing lawns.
• Step 2: Calculate expenses by subtracting the amount spent on mp3s.
• Step 3: Determine the savings by allocating a portion of the remaining money to his savings account.
• Step 4: Identify the remaining funds after saving.
• Step 5: Add any additional earnings to find the total amount Fred keeps.

Following step-by-step solutions allow you to follow the logical process needed to reach the correct answer. This kind of methodical thinking can be applied to various types of problems, not just financial ones.

Basic Arithmetic Operations

Basic arithmetic operations such as addition, subtraction, and division are fundamental in solving everyday mathematics problems. In Fred's scenario:

• The subtraction operation was used when Fred spent part of his earnings on mp3s.
• The division operation helped to decide how much money to put into savings as Fred chose to save half of his remaining money.
• Finally, addition was utilized when Fred gained extra money from washing a car.

These basic arithmetic operations are the building blocks for more advanced mathematics and are indispensable in tackling word problems that involve managing finances. Understanding how to apply these operations in context allows you to solve similar problems in your daily life, ensuring that you can efficiently manage and calculate your finances. Always remember to carry out operations in the correct order to ensure accurate results.