Problem 53 - Fundamentals of Mathematics

Question

A person borrows $$\$ 11$$ on Monday and then pays back $$\$ 8$$ on Tuesday. How much does this person owe?

Step-by-Step Solution

Answer

The person still owes $3.

Step 1: Identify the Total Borrowed Amount

The person initially borrows $11 on Monday. This amount can be considered as a total debt or money owed to someone on Monday.

Step 2: Determine the Amount Paid Back

On Tuesday, the person pays back $8. This amount will reduce the total debt or money owed.

Step 3: Calculate Remaining Debt

To find out how much the person still owes, subtract the amount paid back from the initial borrowed amount. This can be expressed as: \[ \text{Remaining Debt} = \text{Initial Debt} - \text{Amount Paid Back} = 11 - 8 \]

Step 4: Finalize the Calculation

Perform the subtraction: \[ 11 - 8 = 3 \]Thus, after paying back \(8, the person still owes \)3.

Key Concepts

Borrowing and Lending Basics

Borrowing and lending are fundamental activities in personal finance and everyday life. When you borrow money, you receive funds that you agree to pay back in the future, usually with some conditions. In our example, the person borrowed $11, which means they received this amount upfront. Lending, on the other hand, is the act of giving away a sum that you will receive back later. In this scenario, the lender is the party that gave the $11. Understanding this concept helps in managing money and debt efficiently:

• Borrowing: You take money now and promise to repay it later. Often involves interest or other conditions.
• Lending: You provide money to someone now and expect repayment, often with interest.

In borrowing, clarity in conditions, such as how much, when to repay, and at what rate, can prevent issues later on.

Understanding Debt Calculation

Debt calculation is all about figuring out what you owe and when. It's critical for budgeting and financial planning.In this exercise, the debt started at \(11. When the person paid back \)8 on Tuesday, it reduced the total money owed.To accurately calculate debt:

• Initial Debt: The full amount borrowed. In this case, \(11.
• Payments Made: Any money you've repaid, such as the \)8.
• Remaining Debt: Initial debt minus the payments made.

The calculation can be summarized by: \[ \text{Remaining Debt} = \text{Initial Debt} - \text{Amount Paid Back} \] Which simplifies to: \[ 11 - 8 = 3 \] This means the person still owes $3 after the payment.

Basics of Subtraction

Subtraction is one of the four fundamental arithmetic operations. It helps to determine the difference between two numbers. In our example, subtraction is used to calculate how much debt remains after a repayment.When you subtract, you're really just removing one number from another.

• Step 1: Identify the larger number. This is your starting point, like the \(11 borrowed.
• Step 2: Identify the number to subtract, which reduces your starting point. Here, it is \)8.
• Step 3: Perform the subtraction. Subtract 8 from 11 to find what's left: \[ 11 - 8 = 3 \]

This process shows that after paying \(8, the borrower still owes \)3.