Problem 83 - Prealgebra

Question

Checkbook Balance Ethan has a balance of \(40 in his checkbook. If he deposits \)100 and then writes a check for $50, what is the new balance in his check- book?

Step-by-Step Solution

Answer

Ethan's new checkbook balance is $90.

Step 1: Determine Initial Balance

Ethan starts with an initial balance of $40 in his checkbook. This is the amount he currently has before any new transactions are made.

Step 2: Add the Deposit Amount

Ethan deposits \(100 into his checkbook. This increases his balance, so we add this amount to his initial balance. \[ 40 + 100 = 140 \]His balance after the deposit is \)140.

Step 3: Subtract the Check Amount

Next, Ethan writes a check for \(50. This decreases his balance, so we subtract this amount from the balance after the deposit.\[ 140 - 50 = 90 \]The balance after writing the check is \)90.

Key Concepts

Addition

In the context of managing a checkbook, addition is used when you deposit money into your account. A deposit means adding funds, which increases your total balance. For instance, if you have an initial balance of $40 in your checkbook, and you deposit $100, the new balance is calculated by adding the deposit to the initial balance. To compute this, use the addition formula:

• Initial Balance: $40
• Deposit: $100
• New Balance: $40 + $100 = $140

Deposits make your balance grow, which is why addition is such a vital operation in managing your finances. This method helps you keep a running total of the money you have available. Regular deposits ensure there's enough money to cover upcoming expenses or checks, like the $50 check Ethan wrote. Always remember, adding money to your checkbook balance reflects positively. It signifies an increase in the cash available to you.

Subtraction

Subtraction in terms of a checkbook balance refers to the deduction of money whenever an expense, such as writing a check, occurs. Subtraction reduces your total balance. If you want to compute how much money remains after you write a check, you simply subtract the check amount from your current balance. Let's look at an example based on the exercise:

• Current Balance (after deposit): $140
• Check Amount: $50
• New Balance: $140 - $50 = $90

When you write a check for $50, you're effectively distributing that amount out of your account. Subtraction then allows you to see what remains. This process of reducing your balance by subtracting expenses is crucial to avoid overdrawing your account. Each check or payment should be carefully recorded and subtracted from your total to maintain accuracy in your financial records.

Transaction

A transaction in the financial world refers to any action involving money addition or subtraction that affects your account balance. In the context of a checkbook, a transaction could involve depositing money, writing checks, or paying bills, among other possibilities. Transactions are the heartbeat of your financial activity, indicating where and how money flows. The exercise presents two main types of transactions:

• A deposit, which is an addition operation where $100 was added, bringing the balance to $140.
• A payment or check writing, which requires subtraction since $50 was deducted to calculate a new balance of $90.

It's crucial to accurately record each transaction in your checkbook register to maintain control over your finances. This record helps track the inflow and outflow of funds, ensuring that your spending stays within limits and your budget remains balanced. Without careful management of transactions, you risk overspending and potentially incurring bank fees, which could alter your financial stability. Keeping a detailed record ensures accuracy and helps you build good financial habits.